1

Alg2H Chapter 5 Review Date __________ WK #10

1. Given: f(x) = ax2 + bx + c or y = ax

2 + bx + c

Related Formulas: y-intercept: ( 0, ______)

Equation of Axis of Symmetry: x = ______

Vertex: (x,y) = (_________, ____________)

Discriminant = ________________________

x-intercepts:

When the discriminant =____________________,

There are exactly TWO x-intercepts:(________________, 0 and (_______________, 0 )

When the discriminant =____________________,

There is exactly ONE x- intercept: (_________________, 0)

When the discriminant =_____________________,

There are NO x-intercepts

2. GIVEN: y = ax2 + bx + c with following values of a, c and the discriminant

a. For each problem, draw sketches of possible related parabolas. If not possible, state so

and explain why.

b. Determine if the unknown values of a, c or discriminant are < 0, = 0, or > 0

(a) a>0, c<0 (b) a>0, c = 0 (c) a<0, discriminant <0

discrim _____ discrim____ c _________

(d) a<0, discrim =0 (e) a>0, c > 0 (f) a>0, discriminant >0

c ________ discrim ____ c _________

(g) a<0, c=0 (h) a<0, discrim >0 (i) a>0, discriminant =0

discrim _____ c ________ c _________

(j) a<0, discrim<0 (k) discrim = 0, c = 0 (l) a<0, discriminant <0

c ________ a ________ c _________

(m) c=0, discrim<0 (n) discrim = 0, c<0 (o) c<0, discriminant <0

a ________ a ________ c _________

(p) c<0, discrim>0 (q) discrim < 0, c< 0 (r) c>0, discriminant >0

c ________ a ________ c _________

2

3. Given: y – k = a(x – h )2 with the following values of a, h, and k WK #10

a. For each problem, draw sketches of related parabolas. Indicate the vertex, y-intercept,

and any x-intercepts. If not possible, state so and explain why.

b. Determine if the unknown values of a, c or discriminant are < 0, = 0, or > 0

For problems 3i – 3p, determine the quadrant(s) the vertex can be located.

(a) a<0 (b) a<0 (c) a<0 vertex in Quad 1 Vertex in Quad 2 Vertex in Quad 3

h ____k ____ h ____k ____ h ____k ____

(d) a<0 (e) a>0 (f) a>0 vertex in Quad 4 Vertex in Quad 1 Vertex in Quad 2

h ____k ____ h ____k ____ h ____k ____

(g) a>0 (h) a>0 (i) h<0, k>0, a>0 vertex in Quad 3 Vertex in Quad 4 Vertex in Quad ___

h ____k ____ h ____k ____

(j) h<0, k<0, a>0 (k) h>0, k>0, a>0 (l) h>0, k<0, a>0 vertex in Quad__ Vertex in Quad___ Vertex in Quad ___

(m) h>0, k>0, a<0 (n) h>0, k<0, a<0 (o) h>0, k<0, a<0 vertex in Quad__ Vertex in Quad___ Vertex in Quad ___

(p) h<0, k>0, a<0 vertex in Quad__

4. A quadratic in the form 0 = ax2 + bx + c has the following discriminant value.

Select all appropriate “matches” from the column on the right to classify the roots.

a. 27 ______________________________ (1) No real roots

b. –25 ______________________________ (2) 2 Real roots

c. –1 ______________________________ (3) Only one real root

d. 0 _______________________________ (4) Irrational root(s)

e. 36 _______________________________ (5) Rational root(s)

f. 1 ________________________________

3

WK #10

5. Write an equation to represent the 6. Write an equation to represent the quadratic

quadratic function that contains the points function that has a y-intercept of –2 and a

(-3, -47) (2, 3) (5, -15) vertex at (4, 3)

7. Write an equation to represent a quadratic 8. Write an equation to represent the quadratic

function with y-intercept of 2 and function that contains the points

a vertex at (4, 3) (-3, 18), ( 6, -9), and (12, -57)

4

Complete the following without a calculator!!!!!!: WK #10

a) Write the equations in Vertex Form by “completing the square”.

b) Sketch a graph of the equations using the vertex form.

Include: the vertex, axis of symmetry, the y-intercept, and the symmetric point (across from

the y intercept). On the graph, be sure to label the coordinates of each of these points and the

equation of the axis of symmetry.

9) y = x2 + 6x + 5 10) y = 2x

2 – 6x + 9

11) y = -2x2 – 10x – 20 12) y = -x

2 + 7x + 4

Using the given Vertex form, find the x-intercepts in “exact” simplified (radical) form, if

appropriate.

13) y + 12 = (x – 5)2 14) y – 8 = -2(x + 3)

2

5

(page 5) WK #10

Using the given Intercept Form, find the x-intercepts. Plot and label x-intercepts on graph.

Determine, plot and label the axis of symmetry and the coordinates of the vertex. Complete

sketch of graph.

15. y = ¼ (x – 3 )(x + 7 ) 16. y = -.01( x + 4 )( x – 18 )

Write an equation to represent a function that satisfies the stated requirements:

17. x-intercepts of –16 and –2 18. x-intercepts of –2 and 3/8

y-intercept of –64 contains the point ( 1, 25 )

19. Contains the points: 20) Contains the points:

(1, 8 ) (-2, -1) (3, 14) (6, -4 ), (5, 2 ), (6, -1)

6

For problems 21 and 22: WK #10 a)Using the discriminant, determine whether or not the indicated quadratic function ever has the given value of f(x)

(for real values of x)

b) If real values exist, find them by FACTORING whenever the discriminant indicates it is factorable. Otherwise,

find exact values (in simplest radical form) by quadratic formula.

21) f(x) = -12x2 + 21x – 6 f(x) = 3 22) f(x) = -x

2 –6x – 5 f(x) = 2

For problems 23 and 24:

a) From the general form, quickly determine the x-coordinate of the vertex and use it to determine the y-coordinate

of the vertex.

b) Find the value of the discriminant to determine the number of x-intercepts and if their value is rational or

irrational.

c) If they exist, find the x-intercepts

Use factoring, if possible. Otherwise use the quadratic formula and state in “exact” simplified (radical) form.

d) Sketch the graph of each function. Label coordinates of vertex, axis of symmetry, x and y-intercepts, if they

exist, and symmetric point to y-intercept.

23) f(x) = -4x2 + 4x + 15 24) f(x) = 64x

2 – 80x + 25

Complete the following:

25) Given: f(x) = -x2 – x + 1 26) Given: f(x) = -6x

2 – 2x – 3

Find: f(-1) Find: f(-3)