Download Algebra 2A: Ch 4 Test

Algebra 2A: Ch 4 Test Review
Name:
You may prepare a 3 x 5 note card to use during your test (you must hand it in with your test)
You should be able to:
 Graph a quadratic function using at least 3 points, one is the vertex and
one point on each side of it.
 Determine the axis of symmetry and vertex for a standard form
equation.
 Determine the maximum or minimum value for a quadratic function.
 Determine the axis of symmetry and vertex for a vertex form equation.
 Graph an intercept form equation using x intercepts (zeros or roots)
and the vertex.
 Use the FOIL (or double distributive) method to multiply two binomials to
change equations from vertex or intercept form to standard form.
 Solve x2 + bx + c = 0 when a=1 by factoring. Explain what these
solutions describe.
 Solve ax2 + bx + c = 0 by factoring (box method). Explain what these
solutions describe.
 Solve quadratic equations by taking the square root when b = 0
(remember + when solving!!)
 Simplify any radical expression.
 Know what the imaginary number is and how to work with it.
 Add, subtract, multiply, and divide complex numbers (a + bi).
 Use conjugates of radical or complex fractions to simplify,
 Find the absolute value of a complex number.
 Solve quadratic equations with imaginary solutions.
 Complete the square for a quadratic equation.
 Solve quadratic equations by completing the square.
 Rewrite an equation into vertex form by completing the square
 Find the discriminant and use it to decide if there are 2 imaginary, 2 real,
or 1 real solution.
 Use the quadratic formula to solve a standard form equation.
 Graph a quadratic inequality by making it dashed or solid and shading
the appropriate side.
 Graph a quadratic inequality on a number line with open or solid dots
and shade appropriately.
 Decide if a point is a solution to a quadratic inequality.
 Graph a pair of inequalities (2 different inequalities) and shade the
region that is true for both statements.
 Use the vertex and a point to write a quadratic equation in vertex form.
 Use the x-intercepts and a point to write a quadratic equation in
intercept form.
 Use the calculator and 3 points to find a quadratic equation in standard
form.
Practice Problems:
1. Find the axis of symmetry, and vertex for:
a. y = 2x2 – 8 x + 6
b. y = 2x2 – 3
2. Graph the each of the equations in #1, using 3 points.
3.
Find the vertex, axis of symmetry for:
a. y = - 4(x – 2)2 + 4
b. y = (x – 3)(x – 6)
4. Graph each of the equations in #3 using 3 points.
5. Rewrite both equations in #3 in standard form:
6. Factor each of the following equations:
a. x2 – 5 x – 36
b. x2 + 5 x – 14
7. Based on your answers to #6, find the zeros of each.
8. What do these solutions (from #7) represent?
9. Solve the following by factoring:
a. 3 x2 + 7x + 4 = 0
b. 4 x2 + 24 + 20 = 0
10. Put in simplest radical form:
a.
80
b.
7
16
c.
10 15
11. Solve the following:
a. x2 = 169
12. What is the value of i?
13. What is the value of i2 ?
b. -3 x2 = -213
c. 4(x – 1)2 = 8
14. Solve in simplest radical form:
a. x2 = - 13
b. x2 + 11 = 3
c. x2 – 8 = - 36
15. Simplify the following:
a. (8 – i) + (5+ 4i)
b. (7 – 6i) – (3 – 6i)
c. 4i ( -6 + i)
d. (9 – 2i)(-4 + 7i)
e.
5
1 i
f.
4  9i
12i
16. Find the absolute value of each complex number:
a. |4 – i|
b. |2 + 5i|
c. |- 4i|
17. Find the value of c to complete the square then rewrite it as a square
binomial:
a. y = x 2 – 18 x + c
b. y = x 2 – 2 x + c
18. Solve by completing the square:
a. y = x 2 + 4 x – 5 = 0
b. x 2 + 10 x + 5 = 44
19. Rewrite in vertex form by completing the square:
a. y = x 2 – 8 x + 19
b. y = x 2 – 4 x – 1
20. Use the discriminant to decide how many solutions (and if they are real or
imaginary) for each:
a.
x 2 – 8 x + 17 = 0
c. y = x 2 – 8 x + 15 = 0
b. x 2 – 8 x + 16 = 0
21. Solve using the quadratic formula:
a. x 2 – 4 x – 5 = 0
b. 8x 2 – 8 x + 2 = 0
22. Graph the inequalities and shade the appropriate region (both on the x
and y axis and on a number line)
a. y < x 2 – 4x + 3
b. y > x 2 – 4
c. y< -2x 2 + 7x + 4
23. Given x intercepts 4 and 2 and point (3, -2) find the equation for the
quadratic function in intercept form.
24. Given the vertex (2, 3) and point (0, 5) find the equation for the quadratic
function in vertex form.
25. Use your calculator to find the equation in standard form passing through
the points (-2, 3) (0, 1) and (2, 7).