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
Define Vertex
turning point of a parabola
The coordinates of the y-intercept for the quadratic function: What is the y - intercept?
y=-2x2 + 5x - 7
What is (0,-7)?
Which form of equations should be used to find the x-intercepts?
(Hint: It has parenthesis)
factored form
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
The standard form of a quadratic equation.
What is ax2 + bx + c
Define Zeros
solutions or the x-intercepts of a quadratic function
Find the zeros (x-intercepts) of the following:
y = x2 - 8x - 20
x = 10 and x = -2
{-2, 10}
The vertex for this quadratic function:
y = x2 - 8x - 3
What is (4, -19)?
Is the expression (𝑥−𝑦)2 equivalent to 𝑥2−𝑦2
explain your reasoning
No, its equivalent to x2−2xy+y2
The name of the line that divides a quadratic function exactly in half:
What is the Axis of Symmetry
What are the zeros for the equation
x2 - 49 = 0
x=7 and x=-7
What are the zeros for the equation (x+3)2-9
x=0 and x=-3
Find the coordinates of the y-intercept for the quadratic function:
y=3x2 + 2x - 1
Y-intercept (0, -1)
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 ?
x=-8 and x=-3}
Find the vertex for the quadratic function:
y = x2 + 10x + 6
What is (-5, -19)?
Find the y-intercept and vertex for this quadratic function.
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
When a parabola opens upward, it is positive or negative and is it maximum or minimum?
Positive and minimum
The coordinates of the vertex for this quadratic function:
y = x2 - 4x + 8
What is (2, 4)?
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 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. Approximately how long will it take the rock to reach the ground?
h = 4x2 - 28x
What is x = 7 seconds?