Key Features of the Graph of a Quadratic Function
The Domain for any quadratic function
What is all real numbers?
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = -2,7
What number completes the square?
x2 - 9x + ______
81/4
What is the axis of symmetry of the following quadratic function?
2x2 - 4 = 3x
x = 3/4
What is the quadratic formula?
x = -b +- sqrt(b2 - 4ac) /(2a)
The point at which the parabola changes direction
What is the vertex?
Solve the following quadratic equation by factoring. x2+3x+2 = 0
x = -2,-1
What is the solution to the following equation in simplest form?
x2 = 24
x = +/-2 Sq Rt of 6
What is the y-intercept of the quadratic function?
f(x) =1/2 x2 - 2x +5
Write your answer as an ordered pair.
(0,5)
If the discriminant of a quadratic function is 0, what does it mean about the number of real number solutions?
There is 1 real solution.
A vertical line that slices the parabola in half. Its equation is written as x= , where x is the x value of the vertex
What is the axis of symmetry?
If this equation is solved by factoring, what would the factored equation be?
18x3 - 8x = 0
2x(9x2 -4) = 0
2x(3x+4)(3x-4) = 0
Solve using square root method:
(y - 4)2 = 121
y = -7,15
What are the root (s) of the following equation?
f(x)=2x^2
x = 0
Simplify the expression:
4 +/- sq.rt 80
4 +/- 4 rt5
The solution to a quadratic has three other names. What are they?
X-Intercept, Root, and Zero
Solve the following quadratic equation by factoring. 2x2 - 5x - 3 = 0
x = -1/2 x = 3
Write the equation of a quadratic function that opens downward and has a y-intercept of 3
varies
When using the graphing calculator, what calculator function can you use to see the vertex of a parabola that opens downward?
2nd TRACE, 4(Maximum)
What is the discriminant of
1/2x2 = 4x +5 ?
26
The range of any quadratic function goes to -∞ or ∞ and starts at what value?
The y value of the vertex
Solve by factoring:
12x2 - 27 = 0
x = 3/2, -3/2
If completing the square, what is the next series of steps in solving?
x2 - 2x - 24 = 0
x2 - 2x = 24
x2 - 2x +1 = 25
(x-1)2 = +/- rt 25
Find the vertex of f(x)=5x2+2x-2
(-1/5,-11/5)
When solving the following quadratic equation by using the quadratic formula, what is the solution right before the final simplifying of the radical?
4x2 - 17x - 15 = 0
x = [17 +/- sq rt(529)]/8