Definitions
Short Answer
Parts of Parabolas
Graphs
Modeling with quadratic functions
100
What do we call the graph of a quadratic function?
The graph of a quadratic functions is called a parabola.
100
Write down a quadratic function that touches the horizontal axis exactly once.
Any quadratic function with vertex lying on the horizontal axis is a correct answer.
100
Find the vertex of the quadratic function. Then, determine whether the function has a maximum or minimum value, and state that value.
f(x) = x^2 + 10
The vertex is (0,10), and the function has a minimum value of 10.
100
What are the x-intercepts of the parabola?
x = -3, x = -1
100
How high did the ball travel?
15 feet
200
What do we call the highest (or lowest) point of a parabola?
The vertex of the parabola.
200
What is the coefficient in a quadratic function that indicates whether the graph opens up or down?
The leading coefficient.
If the leading coefficient is positive, the graph opens up. Otherwise, it opens down.
200
Find the vertex of the quadratic function. Then, determine whether the function has a maximum or minimum value, and state that value.
f(x) = -2x^2 - 4
The vertex is (0,-4), and the function has a maximum value of -4.
200
What is the vertex of the parabola? 
The vertex is (-2, -1).
200
A soccer ball is placed on the ground and then kicked into the air. The height of the ball depends on the horizontal distance from the kicker, and can be modeled by the function
h(x) = -(x - 6)^2 + 16.
What is the maximum height (in feet) reached by the soccer ball, and at what horizontal position (in feet) is the max height reached.
The maximum height is 16 feet, 6 feet from the kicker.
300
What is the degree of a quadratic function.
Degree 2.
300
What is the general form of a quadratic function with vertex (0,0).
Any quadratic function of the form
f(x) = ax^2
has vertex (0,0)
300
Find the vertex of the quadratic function. Then, determine whether the function has a maximum or minimum value, and state that value.
f(x) = -6x^2 - 4x - 5
The vertex is (-frac{1}{3}, -\frac{13}{3}) , and the function has a maximum value of -\frac{13}{3} .
300
Write the quadratic function for the parabola.
f(x) = (x - 2)^2 - 3
300
Jim wants to build a rectangular enclosure for pigs. He wants the enclosure to be w feet wide, and 20 - w feet long. Find the maximum area of the enclosure.
100 ft2
400
What is the line of symmetry of a parabola?
The line of symmetry is the vertical line that passes through the vertex and splits the parabola exactly in half.
400
What point must the line of symmetry of any parabola pass through?
The line of symmetry is a vertical line that passes through the vertex.
400
Solve the equation. State how may solutions.
2x2+3=203
x = 10 and x = -10
2 solutions
400
Write the quadratic function (in standard form) for the parabola.
f(x) = -3(x + 1)^2 - 1