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?

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, ∞ )

a² + b²= c²

24² + 7² = c²

c= 25

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.