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