Quadratic Graphs Vocabulary
How many zeros (x-intercepts) does the quadratic function 2x2 - 5x - 3 = 0 have?
What is 2?
The solutions of a quadratic function can be found at this location on the graph.
What is the x-intercept?
The zeros of the quadratic equation 2x2 + x - 3 = 0
What are x = -1.5 and x = 1?
Describe the transformation of y=x2 to
y=(x-4)2+3
Shift Right 4 and Up 3
Evaluate this function with f(-5):
f(x) = 2x2 + 15x
f(-5) = -25
The shape of the graph of a quadratic function is called a?
What is a parabola?
The turning point of the quadratic function y = 5x2 + 10x - 2 has a maximum/minimum point.
What is a minimum point?
Find the x-intercepts of the following:
y = x2 - 8x - 20
What are x = 10 and x = -2?
Describe the transformation of y=x2 to
y=-(x+2)2+5
Reflected across the x-axis
Left 2
Up 5
Evaluate this function with f(7):
f(x) = -x2 + 3x
f(7) = -28
The name of the line that divides a quadratic function exactly in half.
What is the axis of symmetry?
This form of a quadratic function reveals the zeros.
What is the Factored Form?
What are the solutions to the equation 2x2 - 2x - 12 = 0?
x = -2, x = 3
f(x) is shifted left 6 units
Two ordered pairs (-2, 15) and (0, 5) are on a parabola. What is the average rate of change between the points?
What is -5?
The name of the point on a quadratic function that will be the maximum or minimum of the function.
What is the Turning Point or vertex
For : y = x2 - 6x + 5
a) state the zeros
b) state the vertex
c) state the y-intercept
a) x = 5 and x = 1?
b) Vertex (3, -4)
c) (0,5)
The expression -x2 + 70x - 600 represents a company's profit for selling x items. For which number(s) of items sold is the company's profit equal to $0?
What are 10 items and 60 items?
Describe how the graph of g(x) = -3x2 compares to the graph of f(x) = x2.
g(x) is a vertical stretch by a factor of 3 and a reflection across the x-axis.
What is the range of the graph of f(x) = 2(x2 - 14x + 48) written in interval notation?
[-2, infinity)
When the parent graph has vertical shifts (up or down), horizontal shifts (left or right), reflections across the x-axis, stretches (vertical or horizontal), and compressions (vertical or horizontal), the graph is said to have performed a?
What is a transformation?
Write the quadratic function f(x) = 5x2 - 40x +88 in vertex form.
f(x) = 5(x - 4)2 + 8
An object is thrown into the air with an initial velocity of 5 m/s from a height of 9m. The equation h(t) = -4.9t2 + 5t + 9 models the height of the object in meters after t seconds. About how many seconds does it take for the object to hit the ground? Round your answer to the nearest whole number.
What is about 2.0 seconds?
The graph of f(x) = -0.25x2 - 2x +1 opens down and has an end behavior where as x increases, f(x) decreases, and as x decreases, f(x) _______________???
Fill in the blank with decreases or increases
What is decreases?
A rectangular floor has an area of 72 square meters. The length of the floor is 6 meters longer than its width.
What are the dimensions of the floor?
width = 6 meters
length = 12 meters