Unit 2 Review
Write the formulas below.
Standard Form
Y-intercept
Vertex
Use the formulas above to help with question 1.
1. Graph f(x) = –5𝑥 2 + 10x, labeling the y-intercept, vertex, and axis of symmetry.
How do you determine a
maximum or minimum
of a quadratic?
Maximum is when a is…
Minimum is when a is…
Axis of Symmetry
1.
How do you find the
value of a maximum or
minimum?
2. Determine whether f(x) = –3𝑥 2 + 6x + 1 has a maximum or a minimum value and find that value.
What is a root, zero or solution of a quadratic look
like on a graph?
List out the steps in order to find the roots by using
your graphing calculator.
3. Solve 𝑥 2 = 6x – 8 by graphing. If exact roots cannot be found, state the
consecutive integers between which the roots are located.
3.
4. Which of the following functions has the same set of zeros as y = x2 + 8x + 15?
a. f(x) = x2 + 16x + 15
c. h(x) = x3 + 8x2 + 15x
b. g(x) = 2x2 + 16x + 30
d. j(x) = x + 5
Below, list the steps how to factor using each method.
GCF
Difference of Squares
Trial and Error
Slide and Divide
5. Solve 3𝑥 2 + 7x = 6 by factoring.
If I am given roots, how to create the factored form of the quadratic?
Once I’ve created the factored form of the quadratic, how do I multiply both factored forms to create a
quadratic equation?
3
6. Write a quadratic equation with –6 and as its roots. Write the equation in the form a𝑥 2 + bx + c = 0, where a, b,
4
and c are integers.
Provide the steps:
What are the steps of completing the square?
What are the steps for using the Quadratic Formula?
For Questions 7 and 8, solve each equation by completing the square.
7. 𝑥 2 + 4x – 9 = 0
8. 𝑥 2 + 8x – 2 = 0
9. Find the exact solutions to 5𝑥 2 = 3x – 2 by using the Quadratic Formula.
Provide the formula of the Quadratic Formula:
Provide the formula of the discriminant, and how to
determine the number and types of roots for the
equation:
For Questions 10 and 11, find the value of the discriminant for each quadratic equation. Then describe the
number and type of roots for the equation.
10. 9𝑥 2 – 12x + 4 = 0
11. 4𝑥 2 + 1 = 9x – 2
Using vertex form, provide the given information:
Vertex Form
Vertex from Vertex Form
Axis of Symmetry from
Vertex Form
Direction of opening
from Vertex Form:
2
12. Identify the vertex, axis of symmetry, and direction of opening for y = – 3 (𝑥 + 5)2 – 7.
Provide the steps in changing a quadratic from standard form INTO vertex form:
13. Write y = 𝑥 2 – 12x + 15 in vertex form.
Describe the following ideas below from vertex form:
Horizontal Shift:
Vertical Shift:
Reflection:
Dilation:
14. Decribe the shift from y  3( x  2) 2  3 to the equation y  3( x  1)2  1 .
15. Write the function that represents the gaph of y  3x 2  4 shifted 2 to the right and up 3.
When given a word problem…What does it really mean when asked to…
Find the maximum height reached?
When will it hit the ground?
16. PHYSICS A rocket is launched from a height of 35 ft with a velocity of 50 ft/sec. The motion can be modeled by
the equation h(t) = 16t 2  v0t  h0 .
A. Find the maximum height reached by the rocket.
B. When will it hit the ground?
When graphing an quadratic inequality…
What point should you test to determine where you
shade?
What inequalities mean a dashed line?
What inequalities mean a solid line?
17. Graph y > 𝑥 2 + 4x – 5 .
17.
What are the steps when solving an inequalitiy:
What inequalities symbols result in two separate
inequalities?
What inequalities symbols result in one compound
inequality?
What methods could you use to find the solutions to
the inequality?
18. Solve the inequality x 2  3 x  2  0
On you graphing calculator, how do I plug in an equation?
What buttons do I press to graph the equation?
19. How many times will the graph of y = x2 – 7x + 8 intersect the x-axis?
a. 0
b. 1
c. 2
d. 4
20. The manager of a symphony computes that the symphony will earn 40 P 2  1100 P dollars per concert if the
charge P for tickets. What ticket price should the symphony charge in order to maximize profit?
Describe the following:
Complex Numbers /
Imaginary Numbers
Addition or Subtraction
of Complex Numbers:
Multiplication of
Complex Numbers:
Division of Complex
Numbers: