Chapter 5 Exam Review
y = !2x +
Consider the quadratic equation:
1.) The above equation is in ____________ form.
2.) Find the vertex.
2
x +1
3.) Find the x-intercepts of the equation by using the completing the square method.
Simplify your answer.
4.) Find the discriminant. How many x-intercepts does this indicate ?
5.) Verify the above x-intercepts by using the quadratic formula. Simplify.
6.) Is the equation factorable ?
If so, verify the x-intercepts by factoring to solve.
7.) Can you isolate x to solve ? If so, isolate x to solve. If not, explain why you cannot.
8.) Put the above equation in vertex form. Verify that the vertex is the same as in #2.
9.) Show how to find the EXACT x-intercepts from the vertex form of the equation in #8.
10.) Graph y = !2x 2 + x + 1 using the information from above AND
by plotting two OTHER points on the graph.
11.) Use your graphing calculator to verify that you found the
correct vertex and x-intercepts.
Chapter 5 Exam Review
Consider the quadratic equation:
y = !3(x ! 2)2 + 5
1.) The above equation is in ____________ form.
2.) Find the vertex.
3.) Find the EXACT x-intercepts of the equation.
4.) Write the above equation in standard form.
5.) Find the discriminant. How many x-intercepts does this indicate ?
6.) Verify the above x-intercepts by using the quadratic formula. Simplify.
7.) Is the equation factorable ?
If so, verify the x-intercepts by factoring to solve.
8.) Graph y = !3(x ! 2) + 5 using the information from above AND
by plotting two OTHER points on the graph.
2
9.) Use your graphing calculator to verify that you found the
correct vertex and x-intercepts.
Chapter 5 Exam Review
y = 2x ! 8
Consider the quadratic equation:
1.) The above equation is in ____________ form.
2.) Find the vertex.
2
3.) Find the discriminant. How many x-intercepts does this indicate ?
4.)
Verify the above x-intercepts by using the quadratic formula. Simplify.
5.) Is the equation factorable ?
If so, verify the x-intercepts by factoring to solve.
6.) Can you isolate x to solve ? If so, isolate x to solve. If not, explain why you cannot.
7.) Put the above equation in vertex form. Verify that the vertex is the same as in #2.
8.) Graph y = 2x 2 ! 8 using the information from above AND
by plotting two OTHER points on the graph.
9.) Use your graphing calculator to verify that you found the
correct vertex and x-intercepts.
Chapter 5 Exam Review
Graph the system of quadratic inequalities.
y > !x 2 ! 4x
y " x 2 + 7x + 10
Solve the quadratic inequalities.
x 2 ! 7x < !4
!x 2 + x + 6 " 0
Write a quadratic function whose graph has the given characteristics.
Vertex ( -3, 2)
Vertex (4, 5)
Point: ( -1, -18)
Point: (8, -3)
A baton twirler tosses a baton into the air. The path of the baton can be modeled by
y = !16x 2 + 45x + 6 where y is the height of the baton from the ground (in ft) at a
horizontal distance of x ft from the twirler. Find the horizontal distances of the baton
from the twirler when it is 35 ft above the ground.