Algebra 2 Quadratic Skills and Concepts

How do you know when to use the AC method?

"a" is a number other than one

The vertex of y = (x-5)^2 + 7 is?

(5,7)

The vertex of x = (y-5)^2 + 7 is?

(7,5)

How do you add or subtract expression with i?

-Combine like terms -Remember to distribute the negative if it is minus -You should always end up with a +bi never anything more

What are the steps to solving by the quadratic formula?

-Enter the discriminant in the calculator -Take the square root if you can and find your two answers (rationals) -If not, do the factor tree and look for pairs to simplify the radical and take an "i" out if needed - seperate the two top parts over the bottom - reduce any fractions you can - make sure its in a + bi order

How do you multiply two expressions with i?

-FOIL/Distribute -Replace any i squared with (-1) -You should always end up with a +bi never anything more

What are the different methods of solving a quadratic?

-Graphing (looking for x-intercepts) -Factoring (setting each factor equal to zero) -Completing the square (doing the process, taking the square root of each side, and simplifying) - Square root method (getting the X^2 and number on the opposite side and taking the square root) - Quadratic formula (good for decimals, big numbers, and things that can't be factored) - Graphing or Plysmlt on the calculator

How do you divide two expressions with i?

-Multiply the top and the bottom by the conjugate of the bottom -Replace any "i squared" with (-1) - The bottom will always simplify to one number - Split multiple parts of the top over the bottom -You should always end up with a +bi never anything more

If the discriminant is zero, what number and type of solutions are there?

1 real rational solution

How do you graph a function written in standard form?

1. Use -b/2a to find the x-coordinate of the vertex. 2. Plug it in find the y-coordinate of the vertex. 3. Draw the axis of symmetry 4. Find the y-intercept by looking at the end number. 5. Reflect the y-intercept to get another point

If the discriminant is negative, how many and what type are the solutions? What would the graph look like?

2 complex The graph wouldn't touch the x-axis

If the discriminant is positive and a not a perfect square, you will have?

2 real irrational solutions

If the discriminant is positive and a perfect square, you will have?

2 real rational solutions

If you have two square roots with negatives in them and you multiply them, will you get a negative or positive?

A negative

If they want the graph, you use _____ to find ____.

A to find P Get the A from the formula Use 1/(4a) = p Move P up/down/forward/back from the vertex by addtin or subtracting it to create the focus and the directrix

What is the domain of a quadratic?

All real numbers

When you "complete the square" to solve you __________ the number in front.

Divide out and take away

How do you find a high power of i?

Divide the power by four. Use the remainder to count into the pattern.

How do you find the y-intercept of a quadratic if it is in standard form?

End number

How do you check an i problem on the calculator?

Enter it directly with the "i" button

A negative in front means

Faced down/max

A positive in front means

Faced up/min

When you "complete the square" to put an equation in vertex form, you __________________ the number in front.

Factor out but leave in front of the parentheses (This influences what you will add to the other side)

How do you find when or where the maximum occurred?

Find the vertex using -b/2a and pick the x-coordinate

How do you find the maximum height?

Find the vertex using -b/2a and pick the y-coordinate

What do you always check for first when factoring?

GCF

If you have something with 2 terms, what are the 2 different ways you might be able to factor it?

GCF and difference of squares

How do you check your answers for the quadratic formula on the calculator?

Graph and look at x-intercepts or use the Plysmlt app. If there are complex solutions, quit out of the app to check to see if the numbers match the decimal.

How do you check if you have the right vertex?

Graph on the calculator and calculate or eyeball the maximum/minimum

How do you check on the calculator whether you have successfully changed to vertex form or standard form?

Graph the original equation and the new equation and check to make sure they are the exact same graph.

How do you multiply two square roots?

Make a factor tree for each and then look at it like one big factor tree. DO NOT multiply the two numbers together.

How do you do a rectangle problem?

Make the width x, express the length in terms of X (such as 2X -3 if it says the length is 3 less than twice the width), distribute the X times the length expression to get a quadratic. Set the quadratic equal to the area number given. Set equal to zero and solve.

What are the steps of the AC method?

Multiply the AC (remember the sign) Find your two numbers Make 4 terms Group GCF of first set Copy what is left and figure out what goes in front of it Right your final factors.

Once you find your two numbers in the AC method, can you go straight to writing your factors?

No

If they want the formula, you use _____ to find ____.

P to find A Figure out how far either the focus or directrix is from the vertex or half of the way between the focus and directrex, that's the P Use 1/(4a) = p with the p you know to find A Put A in the formula

How do you find the y-intercept of a quadratic if it is in vertex form?

Plug zero in for x and calculate

What does it mean when it says "find when the object will be at a certain height?"

Set the formula equal to the height so you can find the x intercepts by factoring with a GCF or using the quadratic formula. You should get 2 answers.

What does it mean when it says "find when the object will hit the ground?"

Set the formula equal to zero so you can find the x intercepts by factoring with a GCF or using the quadratic formula. You should get 0 and another answer that makes sense.

How do you write a quadratic equation in standard form with the given roots?

Set up 2 factors each with the opposite sign of the root Clear any fractions by multiplying everything in that factor by the denominator.

What does maximum or minimum value mean?

The y-coordinate of the vertex. The height in a projectile motion problem

How do you know to use the square-root method to solve a quadratic.

There will only be two terms - a squared and a number. OR It will look like vertex form (like after completing the square)

How do you find "a" in a vertex/focus/directrix problem vs. a point problem?

Use 1/(4a) = p in a vertex/focus/directrix problem Plug the x and y of the point into the equation to solve for A in a point problem

How do you graph to find roots?

Use the vertex, y-intercept, and reflection point to graph. Find the numbers where the graph crosses the x-axis. If it is between two numbers, for each one, write ____ < x < ______ .

How do you find the range of a quadratic?

You look at the vertex (which you find from -b/2a or by looking at vertex form) and whether the parabola is faced up vs. down. Faced up: y>the y of the vertex Faced down: y<the y of the vertex

What is the pattern for the first 4 powers of i?

i/-1/-i/1

Turning improper fractions into ___________________ can help you figure out where they are located on the graph.

mixed numbers

If the number is attached to its variable, use the __________ sign for the vertex.

opposite

If the number is not attached to its variable, use the __________ sign for the vertex.

same

Which variable the number is attached to determines if the number goes in the x or y slot of the _______________.

vertex

What are the different names for the answers to a quadratic?

x-intercepts, roots, zeros, solutions

If you have x=y^2, the axis of symmetry will be _____ and the directrix will be _______

x= y=

If you have y=x^2, the axis of symmetry will be _____ and the directrix will be _______

y= x=