algebra 1a - unit 5: quadratic equations, part 1

what are the coordinates for the vertex of the parabola represented by the quadratic equation y = 1/2(x + 4)^2 − 2?

(-4, -2)

match each quadratic equation with the correct solutions.

(2x - 3)(x + 6) = 0 : x = 3/2 and x = -6 (2x + 3)(x - 6) = 0 : x = -3/2 and x = 6 (3x - 2)(x + 6) = 0 : x = 2/3 and x = -6 (3x + 2)(x - 6) = 0 : x = -2/3 and x = 6

what are the coordinates for the vertex of the parabola represented by the quadratic equation y = −(x − 3)^2 + 5?

(3, 5)

the zeros of a quadratic function are located at x = −8 and x = 4. which expression represents such a function?

(x + 8)(x - 4)

which of the following equations is equivalent to x^2 − 8x = 16?

(x - 4)^2 = 32

use the expression x^2 − 18x − 6 to answer the following questions. what expression is equivalent to the given expression after completing the square?

(x − 9)^2 − 87

how long after emilio throws the marshmallow does it reach its maximum height?

1/4 seconds

emilio throws a marshmallow into the air from his balcony. the height of the marshmallow (in feet) is represented by the equation h = −16t^2 + 8t + 48, where t is the time (in seconds) after he throws the marshmallow. how long does it take the marshmallow to hit the ground, where h = 0?

2 seconds

which expression correctly rewrites 2x^2 − 24x − 30 using the zero trick? make sure the terms are the correct order.

2(x^2 − 12x + 36 − 36 − 15)

solve the quadratic equation −4x^2 + 6x + 16 = 0 by completing the square. which expression represents the correct solutions of the equation?

3±√73/4

a rectangle has a length that is 10 less than 3 times the width. if the rectangle has an area of 8 square feet, what is the width of the rectangle?

4 feet

solve the quadratic equation −x^2 + 8x − 4 = 0 by completing the square. what are the solutions of the equation?

4 ±2√3

emilio throws a marshmallow into the air from his balcony. the height of the marshmallow (in feet) is represented by the equation h = −16(t − 1/4)^2 + 49, where t is the time (in seconds) after he throws the marshmallow. what is the maximum height of the marshmallow?

49 feet

rewrite the expression 5x + 20x + 30 by completing the square.

5(x + 2)^2 + 10

there are three consecutive odd integers where the product of the first and second integers is 1 less than 4 times the third. what three consecutive odd integers fit this description? select all that apply.

5, 7, and 9 -3, -1, and 1

what are the solutions of the equation x^2 = 25/36

5/6,-5/6

what are the solutions of the equation x^2 = 49/100?

7/10,-7/10

what are the solutions of the equation x^2 + 15 = 79?

8,-8

what two positive consecutive integers have a product of 72?

8,9

which expression needs to be added to x^2 − 18x − 6 to complete the square?

81 - 81

the combined area of the photo and the mat needs to be 224 square inches. part a: which equation represents the combined area of the photo and the mat? part b: what is the factored form of the equation that represents the combined area of the photo and the mat?

a: (8 + 2w)(10 + 2w) = 224 b: 4(w − 3)(w + 12) = 0

use the expression x^2 + 10x − 13 to answer the following questions. part a: what numeric expression should be added in order to complete the square for the given expression? part b: what expression is equivalent to the given expression after completing the square?

a: 25 - 25 b: (x + 5)^2 - 38

use the equation y = x^2 − 3x + 2 to answer the following questions. part a: what numeric expression should be added in order to complete the square for the given equation? part b: what equation is equivalent to the given equation after completing the square?

a: 9/4 - 9/4 b: y = (x - 3/2)^2 - 1/4

the product of two positive consecutive integers is 72. part a: which quadratic equation represents the product, where n represents the smaller integer? part b: what is the factored form of the equation that represents the product?

a: n(n + 1) = 72 b: (n + 9)(n − 8) = 0

there are three consecutive odd integers where the product of the first and second integers is 1 less than 4 times the third. part a: which equation represents the verbal description, where n represents the smallest integer? part b: what is the factored form of the equation?

a: n(n + 2) = 4(n + 4) − 1 b: (n + 3)(n − 5) = 0

ashton says that the zeros of the equation y = 6x^2 − 5x − 25 are at x = 5/2 and x = −5/3 which statement correctly describes ashton's claim?

ashton is correct. the quadratic expression has the factors (2x − 5) and (3x + 5), so the zeros are at x = 5/2 and x = −5/3.

lesson 23

completing the square

lesson 22

graphing a factored quadratic

justin launches a water balloon vertically from a platform on his roof. the height of the balloon (in feet) is represented by the equation h = −16t^2 + 32t + 48, where t is the time (in seconds) after he launches the water balloon. what is the vertex form of the equation that represents the height of the water balloon, h, after t seconds?

h = -16(t - 1)^2 + 64

emilio throws a marshmallow into the air from his balcony. the height of the marshmallow (in feet) is represented by the equation h = −16t^2 + 8t + 48, where t is the time (in seconds) after he throws the marshmallow. what is the vertex form of the equation that represents the height of the marshmallow, h, after t seconds?

h = -16(t - 1/4)^2 + 49

what mistakes did he make, and what are the correct solutions of the equation 4x^2 − 24x − 16 = 0.

his final answer in step 7 should have been x = 3±√13 in step 2, nando divided 4x^2 − 24x by 4, but he should have also divided 16 by 4. in step 6, nando added 3 to the left side of the equation, but he subtracted 3 from the right side.

which graphs are parabolas? select all that apply.

https://cdstools.flipswitch.com/asset/media/947706 https://cdstools.flipswitch.com/asset/media/947710 https://cdstools.flipswitch.com/asset/media/947713 https://cdstools.flipswitch.com/asset/media/947712

find the coordinates of the zeros and the vertex in order to graph the parabola represented by the equation y = −(x − 1)(x − 5). which figure shows the zeros, vertex, and parabola graphed correctly?

https://cdstools.flipswitch.com/asset/media/949691

factor the expression 4x^2 − 8x − 54 and find the coordinates of the zeros and the vertex in order to graph the parabola represented by the equation y = 4x^2 − 8x − 5. which figure shows the zeros, vertex, and parabola graphed correctly?

https://cdstools.flipswitch.com/asset/media/949696

which graph correctly represents the quadratic equation y = 1/2x^2 + x − 5/2?

https://cdstools.flipswitch.com/asset/media/950672

what mistake, if any, did sam make?

in step 1, she incorrectly factored out 12. she should have written y = 1/2(x^2 − 4x + 6).

what mistake, if any, did cruz make?

in step 2, he incorrectly added 4 and −4. he should have written −3(x^2 − 2x + 1 − 1) + 8.

what mistake, if any, did cedric make?

in step 3, he incorrectly wrote the square as (x + 4)^2. he should have written x − 4^2.

what mistake, if any, did jordan make?

jordan did not make a mistake.

what mistake, if any, did lara make?

lara should have added rectangles with areas of 3.5x square units and 3.5x square units instead of 4x square units and 3x square units.

lesson 21

solving quadratic equations by factoring

lesson 24

solving quadratic equations by taking square roots

leilani launches a rubber ball vertically from a cliff that overlooks the ocean. the height of the ball in feet t seconds after she launches the ball can be represented by the equation h = −16t^2 + 96t + 100. which statement correctly describes the maximum height of the ball?

the ball reaches a maximum height of 244 feet 3 seconds after she launches the ball.

which statements are true about the parabola represented by the equation y = −7x^2 + 15x + 28? select all that apply.

the parabola has a maximum. since a < 0, the parabola opens down.

which statements are true about the parabola represented by the equation y = 3x^2 − 15x + 30? select all that apply.

the parabola has a minimum. the leading coefficient is positive, so the parabola opens up.

which statements are true about the parabola represented by the equation y = 2/5x^2 + 4/3x + 6/7? select all that apply.

the parabola has a minimum. since a > 0, the parabola opens up.

lesson 25

the vertex form of a quadratic equation

what are the solutions, if any, of the equation x^2 + 38 = 16?

this equation has no real solutions.

what is the equation for the line of symmetry of the parabola represented by the equation y = 2x^2 + 28x + 96?

x = -7 (don't use space)

match each table of values with the correct graph.

x = -8, y = -6 : https://cdstools.flipswitch.com/asset/media/947746 x = -8, y = 6 : https://cdstools.flipswitch.com/asset/media/947748 x = -6, y = 6 : https://cdstools.flipswitch.com/asset/media/947749 x = -6, y = -6 : https://cdstools.flipswitch.com/asset/media/947751

what are the zeros of the quadratic equation y = 5(2x − 1)(x + 3)?

x = 1/2 x = -3

what are the solutions to the quadratic equation 12x^2 + 14x − 6 = 0?

x = 1/3 x = -3/2

what is the equation for the line of symmetry of the parabola represented by the equation y = x^2 − 5x − 6?

x = 2.5

what are the solutions of the equation (x − 21)^2 = 28?

x = 21 + 2√7 x = 21 - 2√7

solve the quadratic equation 8x^2 + 20x = 48 by factoring. what are the solutions? select all that apply.

x = 3/2 x = -4

what are the solutions to the quadratic equation 0 = (x − 4)(x + 2)?

x = 4 x = -2

what are the solutions of the equation (x − 9)^2 = 25?

x = 4 x = 14

solve the quadratic equation x^2 − 4x − 12 = 0 by completing the square. what are the solutions of the quadratic equation?

x = 6 x = -2

what are the solutions, if any, of the equation x^2 − 25 = −7?

x = ±3√2

what are the solutions, if any, of the equation x^2 = 128?

x = ±8√2

what are the solutions, if any, of the equation (x + 49)^2 = 24?

x = −49 ±2√6

match each equation with the figure that shows the zeros, vertex, and parabola graphed correctly for that equation.

y = (2x + 5)(x - 1) : https://cdstools.flipswitch.com/asset/media/950715 y = (x - 5)(x + 2) : https://cdstools.flipswitch.com/asset/media/950718 y = −(x + 5)(x − 2) : https://cdstools.flipswitch.com/asset/media/950722 y = −(2x − 5)(x + 1) : https://cdstools.flipswitch.com/asset/media/950725

match each equation in factored form with the correct equation for the line of symmetry of the parabola represented by the equation.

y = (x + 13)(x - 17) : x = 2 y = (x - 10)(x + 20) : x = -5 y = (x - 12)(x - 18) : x = 15 y = (x + 14)(x + 16) : x = -15

which tables of values correctly represent the given quadratic equation? select two that apply.

y = (x − 1)(x + 2) y = 6x^2 − 18x − 3

what is the standard form of the quadratic equation y = −1/2(x + 5)^2 − 10?

y = -1/2x^2 - 5x - 45/2

what is the vertex form of the quadratic equation y = −2x^2 + 16x − 24?

y = -2(x - 4)^2 + 8

what is the standard form of the quadratic equation y = 1/4(x + 12)^2 + 7?

y = 1/4x^2 + 6x + 43

match each equation with the correct table of values.

y = 2x^2 - 8x - 16 : x = -1 y = -6 y = -2x^2 - 8x - 16 : x = -1 y = -10 y = 2x^2 + 8x - 16 : x = 1 y = -22 y = 2x^2 - 8x + 16 : x = -1 y = 26 (be careful and read the table well)

solve the quadratic equation 3x^2 + 8x = 30 by completing the square. which expression correctly represents the solutions of the equation?

−4±√106/3