Question

4. Graph one of your 2nd degree functions from question 1. Identify which function you used and the key features of your graph. Explain how to find them algebraically.

5. Using your graph from question 4, explain whether the average rate of change is increasing or decreasing, from left to right. Justify your observations by comparing the slopes calculated between at least three different pairs of points.

2nd degree function from question 1: y = x^2 -9

Answer 1

so what was the 2nd degree function from question 1 tha you used...?

Answer 2

y = x^2 -9

Answer 3

ok.... so lets start by finding the intercepts

y- intercept .... let x = 0 so y = 0 - 9

which means the y- intercept is at (0, -9)

find the x intercepts let y = 0 and solve for x

0 = x^2 - 9..... so x^2 = 9 then x = -3 and x = 3

the x intercepts are (-3, 0) and (3, 0)

the coefficient of the leading term x^2 is positive, so the curve is concave up.

in general for a curve \[y = ax^2 + bx + c\]

the line of symmetry is \[x = \frac{-b}{2a}\]

in your question a = 1 and b = 0

so the line of symmetry is

\[x = \frac{-0}{2 \times 1} = 0\]

so the line of symmetry for the curve is x = 0

substitute this into the original equation will get the y value for the verrtex.

the x value at the vertex is the value for the line of symmetry.

In this question the vertex and y- intercept are the same.

hope it helps

Answer 4

Ok thanks! That's for number 4? How about number 5?

Answer 5

ok.... here is the graph

Answer 6

explain whether the average rate of change is increasing or decreasing, from left to right. Justify your observations by comparing the slopes calculated between at least three different pairs of points.

Answer 7

iso if you drew a tangent on the left what type of slope does it have?
as it gets closer to the vertex it decreases.... what happens when you move past the veertex to the right...?