Question

The point (4,-2) is the vertex of the graph of a quadratic function. The points (8,6) and (2,0) also fall on the graph of the function.
Part A:Complete the graph of this quadratic function by first finding two additional points on the graph.

Part B:What is the y-intercept of the graph?

Part C:What are the x-intercept?

Part D:Find the interval on which the rate of change is always positive.

Part E:What is the sign of the leading coefficient for this quadratic function? How do you know?

Answer 1

Answer:

Step-by-step explanation:

y = ax² + bx + c

~~~~~~~

(4, - 2), (8, 6), (2, 0)

a(4²) + b(4) + c = - 2

a(8²) + b(8) + c = 6

a(2²) + b(2) + c = 0

16a + 4b + c = - 2 .............. (1)

64a + 8b + c = 6 ............... (2)

4a + 2b + c = 0 ................. (3)

a = 0.5 ; b = - 4 ; c = 6

y = 0.5x² - 4x + 6

Part A: (0, 6), (6, 0)

Part B: (0,6)

Part C: (6, 0)

Part D: [ 4, ∞ )