Algebra I Finals Exam Quizlet Test Review Part #6

+-2

501. The solution to the equation from flaschard, 500, is +-____.

+-3

502. The solution to: 3x^2 - 27 = 0, by using square roots, is +-____.

0

503. The solution to: x^2 - 10 = -10, by using square roots, is ____.

No

504. Does: -5x^2 + 11x = 16, have a solution using square roots? Yes, or, no?

The number of solutions of: x^2 = d, depends on the value of, d. This happens only if x^2 has, 2, solutions. This can be done by using this as your final answer: x = +- the square root of, d.

505. For solving quadratic equations using square roots, remember, though, that the __________er of ___________s of: ____^____ = ____, ___________s on the ___________ of ____. This happens only if ____^____ has ____, _____________s. This can be done by using this as your _______al, ____________er: x = +- the square root of ____.

6, and, -4

506. The solutions to: (x - 1)^2 = 25, by using square roots, are ____ and -____.

4.5 and 1.5

507. The solutions to: 4(x - 3)^2 = 9, by using square roots, are ____.____ and ____.____.

5/2 and -7/2

508. The solutions to: (2x + 1)^2 = 36, by using square roots, are ____/____ and -____/____.

(x - n)^2

509. (____ - ____)^____ is the binomial for solving quadratic equations using square roots.

Takes the square root of each and every single side.

510. This ________s the ___________, __________ of ________ and __________, _____________, __________.

True

511. True or False: Like always, we solve for, x.

+-3.32

512. The solution to: x^2 + 8x = 19, by using square roots, is +-____._______.

5.5 ft.

513. A touch tank has a height of, 3, ft. Its length is, 3, times its width. The volume of the cubic tank is, 270, cubic feet. The length of the tank is ____.____ ft.

16.4 ft.

514. The width of the tank is ______.____ ft.

x = -b +- the square root of b^2 - 4ac/2a

515. The Quadratic Formula, looks like this: x = -____ +- the square root of ____^____ - ____ac/____a.

a, doesn't equal, 0, at all, and b^2 - 4ac > or equal to, 0

516. This is where ____, ___________'t, _______al, ____ at all, and ____^____ - ____ac > or equal to ____.

3/2, and, 1

517. The solutions for: 2x^2 - 5x + 3 = 0, by using the Quadratic Formula, are ____/____ and ____.

The equation needs to be in standard form, like always, and, it looks like this: ax^2 + bx + c = 0. Second, you have to identify all of the, a, b, and, c, values. Third, you need to plug it into the Quadratic Formula. Fourth, you need to split the sign, so that it will look like this: +-. It will somehow look like this: first: x = -b + the square root of b^2 - 4ac/2a, second: x = -b - the square root of b^2 - 4ac/2a. And, fifth, you need to solve for the zeroes to get your final answer.

518. For using the Quadratic Formula, the ________________ needs to be in _______________, ________, like always, and, it looks like this: _______^____ + ____x + ____ = ____. Second, you have to ____________ all of the ____, ____, and, ____, _________s. Third, you need to ________ it _________ the ______________, ________________. Fourth, you need to _________ the ________, so that it will look like this: _____ (2 signs). It will somehow look like this: first: x = -____ + the square root of ____^____ - ____ac/____a, second: x = -____ - the square root of ____^____ - ____ac/____a. And, fifth, you need to _________ for the _________es to _______ your _______al, __________er.

5, and, 1

519. The solutions for: x^2 - 6x + 5 = 0, by using the Quadratic Formula, are ____ and ____.

-1.2 and 1.9

520. The solutions for: -3x^2 + 2x + 7 = 0, by using the Quadratic Formula, are -____.____ and ____.____.

Use it to determine the real number of solutions of a quadratic equation, or, the total number of x-intercepts, of, the graph, of, the related function. There can be either, 2, 1, or, 0, solutions.

521. Since the discriminant is under the radical symbol, you can ________ it to _______________ the _______, ______________er of _________________s of a _________________, _________________, or, the _____al, _____________er of ____-_________________s, of, the ________, of, the ___________ed, _______________. There can be ________er, ____, ____, or, ____, ______________s.

2

522. x^2 + 8x - 3 = 0, has ____ real solutions.

1

523. 9x + 1 = 6x, has ____ real solution.

1

524. -x^2 + 4x - 4 = 0, has ____ real solution.

No

525. Does: 6x^2 + 2x = -1, have a solution(s)? Yes, or, no?

2

526. 1/2x^2 = 7x - 1, has ____ real solutions.

No

527. Does: y = -x^2 + x - 6, have a solution(s)? Yes, or, no?

2

528. y = x^2 - x, has ____ real solutions.

1

529. f(x) = x^2 + 12x + 36, has ____ real solution.

Advantages: 1. Factoring: Straightforward when the equation can be factored, easily, exactly, and, perfectly. 2. Graphing: Can, easily, closely, and, carefully, see the total number of real solutions, used when approximate solutions are sufficient, and can also use a TI-84 CE Graphing Calculator for this as well, too. 3. Using Square Roots: Can be used to solve equations of the form(ula): x^2 = d. 4. Quadratic Formula: Can be used for any specific quadratic equation, and, gives the exact solutions. Disadvantages: 1. Factoring: Some equations aren't factorable at all. 2. Graphing: Can't give exact solutions, anymore, at all. 3. Using Square Roots: Can only be used for certain equations. 4. Quadratic Formula: Takes some time to do calculations.

530. What are the advantages and disadvantages of these, 4, things: 1. Factoring? 2. Graphing? 3. Using Square Roots? 4. Quadratic Formula?

No

531. Does: x^2 = -100, have a solution(s)? Yes, or, no?

7, or, 1

532. The solutions for: (x - 4)^2 = 9, by using square roots, is either ____ or ____.

5, or, -5

533. The solutions for: x^2 = 25, by using square roots, is either ____ or -____.

0

534. x^2 = -36, has ____ solutions.

0

535. x^2 + 200 = 100, has ____ solutions.

5, or, -5

536. The solutions for: x^2 - 10 = 15, by using square roots, is either ____ or -____.

Parabola

537. A type of u-shaped graph of a quadratic function is called a type of ________________.

f(x) = x^2

538. The quadratic parent function is: f(x) = ____^____.

1. -3, 9! 2. -2, 4! 3. -1, 1! 4. 0, 0! 5. 1, 0! 6. 2, 4! 7. 3, 9!

539. The formula from flashcard, 538, plots which, 7, points?

(0, 0)

540. The vertex (origin) of: y = x^2, is always (____, ____).

The lowest point on a type of parabola that opens up, or, the highest point on a parabola that opens down.

541. For real, the vertex, is the ______est, __________ on a _________ of __________________ that _________s, _____, or, the _______est, __________ on a __________________ that _________s, __________.

The vertical line that divides the parabola into, 2, symmetric parts, plus, this also passes through the vertex as well, too.

542. The axis of symmetry is the __________al, _______ that ___________s the _________________ into ____, __________________, _________s, plus, this also __________es through the ____________ as well, too.

Identifying the regions, in which the graph either increases or decreases.

543. Also, you can describe the behavior of the graph, by ___________________ing the __________s, in which the ________ either ______________________s or _____________________s.

y = x^2 decreases for whenever x < 0 and increase for whenever x > 0.

544. Depending on which sign, x, is, to, 0, either greater than or less than, you'll notice that: y = ____^____, _____________________s for whenever ____ < ____ and _______________ for whenever ____ > ____.

Vertex: (-2.5, 0). Axis of Symmetry: x = -2.5. Behavior: Increases x > -2.5, decreases x < -2.5. Domain: All Real Numbers. Range: y > 0.

545 (HARD). The vertex, axis of symmetry, behavior of this graph shown, domain, and, range, is...

Vertex: (0, 0). Axis of Symmetry: x = 0. Behavior: Increases x > 0, decreases x < 0. Domain: All Real Numbers. Range: y > 0.

546. The vertex, axis of symmetry, behavior of this graph shown, domain, and, range, is...

The translation for: g(x) = 3x^2, is a vertical stretch by, 3. The translation for: g(x) = -5x^2, is a vertical stretch by, 5, and a reflection across the x-axis. The translation for: g(x) = 1/10x^2, is a vertical shrink by 1/10. The translation for: g(x) = -0.2x^2, is a vertical shrink by 0.2, and a reflection across the x-axis.

547. The, 4, quadratic functions: 1. g(x) = 3x^2. 2. g(x) = -5x^2. 3. g(x) = 1/10x^2. 4. g(x) = -0.2x^2. ... are graphed, shown on the image. Tell me, what is the translation for each?

The translation for: g(x) = x^2 + 3, is a vertical translation up, 3. The translation for: g(x) = 2x^2 - 2, is a vertical stretch by, 2, and a vertical translation down, 2.

548. What is/are the translation(s) for these, 2, quadratic functions: 1. g(x) = x^2 + 3? 2. g(x) = 2x^2 - 2?

Vertical stretch by, 2, and a vertical translation down, 5.

549. The translations for: g(x) = 2x^2 - 5, are...

Vertical shrink/compression by 1/4, reflection over the x-axis, and a vertical translation up, 4.

550. The translations for: h(x) = -1/4x^2 + 4, are...

Vertical translation down, 7.

551. Let: f(x) = -0.5x^2 + 2, and: g(x) = f(x) - 7. The transformation from the graph of, f, to, g, is a...

g(x) = -0.5x^2 - 5

552. The equation that represents, g, in terms of, x, looks like this: g(x) = -____.____x^____ - ____.

Vertical translation up, 3.

553. Let: f(x) = 3x^2 - 1, and: g(x) = f(x) + 3. The translation from the graph of, f, to, g, is a...

g(x) = 3x^2 + 2

554. The equation that represents, g, in terms of, x, looks like this: g(x) = ____x^____ + ____.

For: y = -16t^2 + 64: 1. 0, 64! 2. 1, 48! 3. 2, 0! For: y = -16t^2 + 144: 1. 0, 144! 2. 1, 280! 3. 2, 80! 4. 3, 0!

555. The function: f(t) = -16t^2 + s0 represents the approximate height, in feet, of a falling object, t, secs., after it is dropped from an initial height, s0, in feet. An egg is dropped from a height of, 64, ft. What are the points for each?

2

556. After ____ secs., the egg hit the ground, perfectly.

3

557. Suppose the initial height is now up to a total of, 144, ft. How many secs. is it now, that, the egg hit the ground, perfectly?

Vertical translation up, 80

558. On a graph, representing that, the translation was a _____________al, ___________________________, _______, ________.

-b/2a

559. The equation for the axis of symmetry, is: -____/____a.

2

560. The axis of symmetry for: f(x) = x^2 - 4x + 2, is ____.

(2, 2)

561. The vertex of it is...

-2

562. The y-coordinate of it is -____.

1. 1, -1! 2. 3, -1!

563. What, 2, points are also included on a graph to represent the equation from flashcard, 560?

1

564. The axis of symmetry for: f(x) = 3x^2 - 6x + 5, is ____.

(1, 2)

565. The vertex of it is...

5

566. The y-intercept is ____.

All Real Numbers

567. The domain of it is...

y > or equal to, 2

568. The range of it is...

-1

569. The axis of symmetry for: f(x) = 3x^2 + 6x + 2, is -____.

(-1, -1)

570. The vertex of it is...

2

571. The y-intercept is ____.

All Real Numbers

572. The domain of it is...

y > or equal to, -1

573. The range of it is...

-2

574. The axis of symmetry for: -2x^2 - 8x - 1, is -____.

(-2, 7)

575. The vertex of it is...

-1

576. The y-intercept is -____.

All Real Numbers

577. The domain of it is...

y < or equal to, 7

578. The range of it is...

Either a maximum or minimum value

579. The y-value of the vertex of a quadratic function either has a ___________________________ or ____________________, ____________.

Maximum

580. When, a, is negative, the y-value has a ______________________ value.

Minimum

581. When, a, is positive, the y-value has a ___________________ value.

Maximum

582. f(x) = -4x^2 - 24x - 19, has a ____________________ value.

(-3, 17)

583. The value is...

Minimum

584. g(x) = 8x^2 + 16x - 2, has a ___________________ value.

(-1, -10

585. The value is...

Maximum

586. h(x) = -1/4x^2 + x - 6, has a ____________________ value.

(0.125, -5)

587. The value is...

Water Balloon, 1: 105, ft. Water Balloon, 2: 125, ft.

588. A group of friends is launching water balloons. The function: f(t) = 16t^2 + 80t + 5, represents the total height, in feet, of the water balloon, t, secs., after it is launched. The height of Water Balloon, 2, t, secs., after it is launched is shown on a graph. What's the total height of both water balloons?

2

589. Water Balloon ____ went higher.

2

590. Water Balloon ____ went in the air longer.

4

591. The axis of symmetry for: g(x) = 1/2(x - 4)^2, is ____.

(4, 0)

592. The vertex is...

1. 0, 8! 2. 2, 2! 3. 6, 2!

593. What are, 3, more points included in it?

Horizontal shift right, 4, vertical compression/shrink by 1/2.

594. The translations for the equation from flashcard, 591, are...

Reflect on each other across the axis of symmetry

595. Points should ______________ on each _______er, ____________ the _________ of ________________________.

-5

596. The axis of symmetry for: h(x) = 2(x + 5)^2, is -____.

(-5, 0)

597. The vertex is...

1. Vertical stretch by, 2. 2. Horizontal translation left, 5.

598. The, 2, transformations for the equation from flashcard, 596, are...

2

599. The axis of symmetry for: j(x) = -(x - 2)^2, is ____.

(2, 0)

600 (MAX). The vertex is...