properties
What is the name of the symmetrical U-shaped curve created by a quadratic function?
Parabola
Factor the expression:
x^2-25
.
(x-5)(x+5)
State the general "Vertex Form" equation of a quadratic function.
y=a(x-h)²+k
Recite the Quadratic Formula used to solve for x.
x = (-b ± √(b²-4ac)) / 2a
In a projectile formula ht, what does h0 represent?
Initial Height
Name the specific point where the parabola changes from increasing to decreasing (or vice versa).
Vertex
Find the binomial factors for the quadratic:
x^2+8x+12
(x+6)(x+2)
Identify the vertex coordinates for the function:
y=x-5^2+8
(5, 8)
Identify the values of a, b, and c for:
-2x^2+4x-9=0
a=-2, b=4, c=-9
A ball is thrown from 6ft height. What is the initial height in the equation?
6 feet
What is the equation of the vertical line that passes through the vertex of a parabola?
Axis of Symmetry
Solve for x:
x^2-5x-14=0
x = 7, -2
Describe the horizontal and vertical shift for
y=x+2^2-7
Left 2, Down 7
Calculate the discriminant for
x^2+6x+9=0
.
D = 0 (One real root)
Calculate the time to reach max height for
h=-16t^2+64t
.
t = 2 seconds
in the standard form y=ax2+bx+c ,what does the constant 'c' represent?
Y-intercept
Use the GCF method to solve the equation:
3x^2+15x=0
x = 0, -5
Does the parabola
y=-4x-1^2+3
open upward or downward? Why?
Down (a is negative)
Solve for x using the formula:
x^2-4x+3=0
x = 3, 1
If a ball's path is h=-t^2+4, when does it hit the ground?
t = 2 seconds
Define the 'discriminant' and explain what it tells us about the roots of the equation.
b²-4ac (Root type)
Factor the complex trinomial where a>1:
2x^2+7x+3
(2x+1)(x+3)
Write the equation in vertex form given vertex 00 passing through point 28.
y = 2x²
Use the formula to find the irrational roots of:
x^2+2x-4=0
.
x = -1 ± √5
Profit Px=-x^2+40x. What unit count x maximizes profit?
x = 20 units