Graphs
Equations
Comparing Quadratics
Word Problems
100
Is the vertex of the parabola below a maximum or a minimum? 
Since the parabola opens downward the vertex is a maximum. 
100
Is the vertex of the function y = 3x2 - 2x - 1 a maximum or a minimum?
The vertex of y = 3x2 - 2x - 1 is a minimum because the a-value of the parabola is positive, so it opens up.
100
Which function has a maximum?
f(x) = x2 - 7x + 3
Since f(x)= x2 - 7x + 3 has a positive a-value it opens up and has a vertex that is a minimum, while g(x) has a vertex that appears to be at (-1, -4) which has a y-value greater than the other y-values. Therefore g(x) has a maximum.
100
A ball is kicked in the air from a height of 2 feet with an initial velocity of 15 feet per second. The equation to model the situation is
h(t) = -16t2 + 15t + 2.
What is the highest point reached by the ball?
The vertex of is h(t) = -16t2 + 15t + 2 is approximately (0.469, 5.516) so the highest point reached by the ball is about 5.5 feet.
200
What are the x-intercepts of the graph shown below?
The x-intercepts of the graph are (-2, 0) & (3, 0)
200
What are the x-intercepts of the function y = x2 - 4.
**Try this without a calculator or desmos!**
The x-intercepts of y = x2 - 4 are (2, 0) & (-2, 0) .
200
Which function has a higher maximum?
f(x) = -x2 - 4x - 1 & g(x) is graphed below.
The vertex of f(x) = -x2 - 4x - 1 is (-2, 3) while the vertex of g(x) is (-2, -2). The maximum refers to the y-value, the highest of which is 3 and so f(x) has the higher maximum.
200
A ball is kicked in the air from a height of 2 feet with an initial velocity of 15 feet per second. The equation to model the situation is
h(t) = -16t2 + 15t + 2.
How long does it take for the ball to reach its highest point?
The vertex of is h(t) = -16t2 + 15t + 2 is approximately (0.469, 5.516) so the highest point reached by the ball occurs about 0.469 seconds after it was kicked.
300
What is the vertex of the parabola shown below?
The vertex of the parabola is (-2, -9)
300
What are the x-intercepts of the function
y = x2 - 4x + 3
**Try this without a calculator or desmos!**
The x-intercepts of y = x2 - 4x + 3 are (1, 0) & (3, 0) .
300
Which function has the smaller y-intercept,
f (x) = -x2 - 4x - 1 or g(x) graphed below?
The y-intercept of f (x) = -x2 - 4x - 1 is (0, -1) & the y-intercept of g(x) is (0, 2) so f(x) has the smaller y-intercept.
300
A ball is kicked in the air from a height of 2 feet with an initial velocity of 15 feet per second. The equation to model the situation is
h(t) = -16t2 + 15t + 2.
How long does it take for the ball to hit the ground?
The x-intercept of is h(t) = -16t2 + 15t + 2 is approximately (1.056, 0) so the ball hits the ground about 1.056 seconds after it was kicked.
400
What is the axis of symmetry of the parabola shown below?
The axis of symmetry of the parabola is x = -2
400
What are the x-intercepts of the function
y = 2x2 - 7x + 3
The x-intercepts of
y = 2x2 - 7x + 3
are (0.5, 0) & (3, 0)
400
Which function has a higher maximum?
f(x) = -x2 - 4x - 7 or
The vertex of f(x) = -x2 - 4x - 7 is (-2, -3) while the maximum of g(x) is (-1, -4). The higher y-value between the 2 is -3, so f(x) has the higher maximum.
400
An object is launched from a platform 15 meters off the ground. It if was of launched with an initial velocity of 11 meters per second. The equation to model the situation is
h(t) = -4.9t2 + 11t + 15.
How long does it take for the object to hit the ground?
The x-intercept of is h(t) = -4.9t2 + 11t + 15 is approximately (3.201, 0) so the object hits the ground about 3.201 seconds after it was launched.
500
Identify all intercepts of the parabola shown (write as ordered pairs).
The intercepts are as follows...
x-ints: (-5, 0) & (1, 0)
y-int: (0, -5)
500
What is the vertex of the function:
y = 2x2 - 4x - 6
The vertex of the function
y = 2x2 - 4x - 6
is (2, -8)
500
Which function has the greatest x-intercept?
f(x) = x2 - x - 6 or
The x-intercepts of f(x) = x2 - x - 6 are (-2, 0) & (0, 3) while the x-intercepts of g(x) are (-2, 0) & (0, 0).
The greater of the x-values is 3, so f(x) has the greater of the x-intercepts.
500
An object is launched from a platform 15 meters off the ground. It if was of launched with an initial velocity of 11 meters per second. The equation to model the situation is
h(t) = -4.9t2 + 11t + 15.
Identify the vertex & the meaning of both numbers of the vertex.
The vertex of h(t) = -4.9t2 + 11t + 15 is approximately (1.122, 21.173).
The 1.122 represents the amount of time it took to reach the maximum after the object was launched.
The 21.173 represents the highest number of meters reached by the object.