Quadratic Basics
Solving by Graphing
Factoring
Direct Method/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
State the GCF of the following numbers:
32, 60
4
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
y = -4(x + 6) - 10
(-6, -10)
200
State the GCF and factor it from the following equation
15x^4-30x^3+10x^2
GCF = 5x^2
Factored form =
5x^2(3x^2-6x+2)
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
State the two forms of quadratics along with their equations
Standard Form. Vertex Form *See Equations*
300
Draw a sketch of the parabola template (scaled correctly) if a = -3
*See Answers*
300
Factor the following equation using the sum-product pattern
x^2+15x+56
(x+7)(x+8)
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 normal
y = -7x^2-4x+5
b. a = -7
c. Opens down
d. Graph has a max
e. Narrower than normal
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
Write an example of a quadratic equation with:
a. 2 solutions
b. No solutions
*See Answers*
500
Using your calculator, Solve the following quadratic equation by graphing. Round to the nearest hundredth
y=3x^2-23x+17
x = 0.83, 6.84
500
Solve the following quadratic by factoring
0 = 6x^2+37x+6
x = -6, -1/6
500
What is sqrt(-25)
Hint: It's not No Solution
+-5i
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