Tredyffrin/Easttown School District
Goal: Review for tomorrow’s quadratics test.
Thinking Skill: Demonstrate understanding of concepts.
Problems 1 – 9 should all be done by hand. The calculator can be used for 10 - 11.
Answers should be left in simplest radical form.
1. Write the equation of the parabola in standard form through the points (2, 7), (-1, 10) and (0, 5). *You will need to use either substitution or elimination.
2. Write the equation of the parabola with a vertex of (3, 1), through the point (-1, -15).
3. Write each of the following equations in vertex form by completing the square (if not done
already). Sketch the graph by determining the vertex, the line of symmetry, the y-intercept, and
the x-intercept(s) if they exist.
a. [pic][pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
b. [pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
c. [pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
d. [pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
4. Graph the following by finding the vertex, y-intercept, axis of symmetry, and one other point.
a. [pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
b. [pic]
Vertex:
Line of Symmetry:
y-intercept:
x-intercepts:
5. Solve each quadratic equation. Use a variety of methods.
a. [pic] b. [pic] c. [pic]
d. [pic] e. [pic] f. [pic]
6. Simplify each expression into a+bi form. Show all work.
a. (8+4i)(1-3i) b. [pic] c. [pic]
d. [pic] e. [pic] f. [pic]
7. Evaluate the discriminant and determine the type and number of solutions.
a. [pic] b. [pic]
8. Write an equation in which the discriminant is equal to -9.
What type of solutions does your equation have?
9. Graph the system of quadratic inequalities. Shade the region and find the intersection points.
[pic]
10. The equation [pic] represents the parabolic flight of a certain cannonball shot at an angle of 26[pic], where y is the height of the cannonball and x is the vertical distance traveled in meters. Try this WINDOW [-5, 60, 5, -1, 10, 1], this follows the order of xmin, xmax etc.
a. What is the maximum height of the cannonball? How do you know? Explain your method.
b. What is the total horizontal distance traveled by the cannonball? How do you know? Explain your method.
11. A rectangular backyard will be fenced in on 3 sides. If there is 200ft of fencing,
a. Determine the dimensions of the fence for the maximum area.
b. Determine the maximum area.
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Date _________ Period_________
U5 D13: Review for Unit 5 Test
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