Quadratic Basics
Solving by Graphing
Factoring/Quadratic Function
Square root/Completing the Square
The Quadratic Formula
100

State the axis of symmetry equation (also used to find the vertex on standard form equations)

x=(-b)/(2a)

100

Solve the following quadratic equation


x = 0, -4

100

Find the solution: x2 - 5x -14

x = 7, x = -2

100

Solve the following equation for x using the direct method


 x^2+15=0 

No Solution

100

State the value of a, b, and c in the equation below

 y = -x+3 

a = 0, b = -1, c = 3

200

If the Vertex is the highest point on a quadratic graph, what do we know about its a-value?

It must be negative

200

State the vertex of the following quadratic equation

 y = -4x^2 - 24x + 10 

(-3, 46)

200

Solve the following quadratic equation.

 x2+3x+2 = 0

x = -2 x = -1

200

Determine the value of c that completes the square

 x^2-14x+ ___

c = 49

200

State the Quadratic Formula

x=(-b+-sqrt(b^2-4ac))/(2a)

300

How do we know a quadratic function does not have solutions when using the quadratic formula?

There will be a negative number under the square root.

300

Draw a sketch of the parabola template (scaled correctly) if a = -3

*See Answers*

300

Solve using the quadratic formula:

 x2 - 6x + 3 = 0

x=3+-sqrt3

300

Solve the following equation using the direct method

 5x^2-80=100

x = +-6


300

The discriminant = 0. What does that tell us about the shape of our quadratic function? 

That it rests perfectly on the x-axis

400

 y = 5-4x-7x^2 

a. Write in standard form

b. a - value

c. Opening up/down

d. Whether the graph has a max/min

e. Wider/Narrower than if a=1

y = -7x^2-4x+5

b. a = -7

c. Opens down

d. Graph has a max

e. Narrower than a=1

400

State the vertex of the following quadratic equation (hint: remember your formula)

 y=3x^{2}-6x+10 

Vertex: (1, 7)

400

Solve the following equation by factoring

  0 = x^2-x-72 

x = +9, -8

400

Solve the following equation by completing the square

 0 = x^2-6x-10 

x = +-sqrt10+3

400

Use the discriminant to find the number of solutions for the following Quadratic

 y=2x^2+12x+19 

No Solutions

500

When solving quadratic equations, what are the other names we learned for x-intercepts?

Hint: there are 4 total

Solutions, Roots, Zeros of a function

500

Describe the transformation using vocabulary words:

Parent function:

x^2+2x+3

Transformed function:

-1/2x^2+2x-4

1. The function is reflected over the x-axis and now opens downward.

2. The function is wider because the absolute value of a decreased.

3. The function is vertically translated down 7 units.

500

Solve the following quadratic by factoring

 0 = 6x^2+37x+6 

x = -6, -1/6

500

Solve the following

x2 - 5x - 24 = 0

x = 8, x = -3

500

Solve the following equation using the quadratic formula. Round your answers to the nearest hundredth

 y = -4x^{2}+17x-11 

x = 0.8, 3.45

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