WK # Given: f(x) = ax2 + bx + c

Transcription

1 Alg2H Chapter 5 Review 1. Given: f(x) = ax2 + bx + c Date or y = ax2 + 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 discrim (b) a>0, c = 0 discrim (c) a<0, discriminant <0 (d) a<0, discrim =0 (e) a>0, c > 0 discrim (f) a>0, discriminant >0 (g) a<0, c=0 discrim (h) a<0, discrim >0 (i) a>0, discriminant =0 (j) a<0, discrim<0 (k) discrim = 0, c = 0 (l) a<0, discriminant <0 (m) c=0, discrim<0 (n) discrim = 0, c<0 (o) c<0, discriminant <0 (p) c<0, discrim>0 (q) discrim < 0, c< 0 (r) c>0, discriminant >0 1

2 3. Given: y k = a(x h ) 2 with the following values of a, h, and k 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 = ax 2 + 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 2

3 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) 3

4 Complete the following without a calculator!!!!!!: 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 ) y = 2x2 6x ) y = -2x2 10x 20 12) y = -x2 + 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 4

5 (page 5) 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 x-intercepts of 2 and 3/8 y-intercept of 64 contains the point ( 1, 25 ) 19. Contains the points: (1, 8 ) (-2, -1) (3, 14) 20) Contains the points: (6, -4 ), (5, 2 ), (6, -1) 5

6 For problems 21 and 22: 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) = -x2 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 ) f(x) = 64x2 80x + 25 Complete the following: 25) Given: f(x) = -x2 x + 1 Find: f(-1) 26) Given: f(x) = -6x2 2x 3 Find: f(-3) 6