Quadratic Graphs
How many zeros (x-intercepts) can a quadratic function have? List all possibilities.
What is 3 possible types of solutions
2, 1, or none
What is the value of "a" for a graph of a quadratic function that is concave down.
"a" is negative
or - a
The coordinates of the y-intercept for the quadratic function: What is the y - intercept?
y=-2x2 + 5x - 7
What is (0,-7)?
If the x-intercepts of a function are x = 6 and x=12, what is the Axis of Symmetry (x-value of the vertex)?
What is x = 9?
An apple is launched directly upward at 64 feet per seconds from a platform 80 feet high. The equation is
h = -16t2 + 64t + 80, where h = height & t = seconds. How many seconds does it take the apple to hit the ground?
What is t = 5 seconds
Standard Form of a quadratic function:
What is ax2 + bx + c
The vertex of the quadratic function
y = 5x2 + 10x - 2 a maximum or minimum point?
What is a minimum?
Find the x-intercepts of the graph of the function:
y = x2 - 8x - 20
(10, 0) and (-2, 0)
The vertex for this quadratic function:
y = x2 - 8x + 12
What is (4, -4)?
Let f(x) be the function; f(x) = 2x2 + 3x -2. The value of the positive.
What is 1/2 (one half)?
The name of the line that divides a quadratic function exactly in half:
What is the Axis of Symmetry
The solutions of the equation x2 - 49 = 0
{7, -7}
What determines whether a function will have a maximum turning point or a minimum point?
Whether or not the coefficient of the x2 term is positive or negative.
Find the coordinates of the y-intercept for the quadratic function:
y=(x-3)2-4
Y-intercept (0, 5)
Evaluate this function with f(-5):
f(x) = 2x3 + 15x
What is f(-5) = -325?
The name of the point on a quadratic function that will be the maximum or minimum of the function?
What is the vertex?
What are the zeros of the equation
y = x2 + 11x + 24 = 0?
{-8, -3}
Find the vertex for the quadratic function:
y = -x2 -6x + 40
What is (-3, 49)?
Find the y-intercept and vertex for this quadratic function (round to nearest tenth).
y = x2 + 49 = 14x
The y-intercept (0, 49) and
the vertex (7, 0)
Evaluate this function with f(7):
f(x) = -x2 + 3x
What is f(7) = -28
The area of the rectangle is 78, the length is x + 7 and the width of x. What is the value of "x?"
What is x = 6
What makes a parabola concave up? When it is concave up, does it have a maximum or minimum?
Positive coefficient of the x2 term.
It has a minimum.
The coordinates of the vertex for this quadratic function:
y = x2 - 16x + 39
What is (8, -25)?
If the x-intercepts of a function are x = 6 and x=-12, what is the Axis of Symmetry (x-value of the vertex)?
x=-3
Bob drops a rock from the Leaning Tower of Pisa (186 feet) in Italy. The height in feet (h) of the fallen rock above the ground is given by the equation below, where "t" represents the time in seconds and "c" is the initial height of the rock. Approximately how long will it take the rock to reach the ground?
h = -16t2 + c
Approximately 3.41 seconds.