Question

7. Consider the function f(x) = -10(x - 5) + 7. Describe the transformation of the graph ofthe parent quadratic function. Then identify the vertex.

Answer 1

Given:

f(x) = -10(x - 5) + 7

Use slope intercept form:

y = mx + b

Find the y-intercept for g(x) = x

The y-intercept, b = 0

Slope, m1 = 1

Find the y-intercept for, f(x) = -10(x - 5) + 7

f(x) = -10x + 50 + 7

f(x) = -10x + 57

y-intercept, b = 57

slope, m2 = -10

We have the following y-intercepts

b1 = 0

b2 = 57

The vertical shift is = b2 - b1 = 57 - 0 = 57

This means there was a transformation of 57 units upward.

Find the vertical stretch:

Since m2 is greater than m1, the graph is vertically stretched

Also, m1 and m2 have opposite signs, this means there was a reflection about the y-axis.

Therefore, the transformations are:

Translated 57 units upward

Vertical stretch

Reflection about the y-axis

The vertex is the point where the fuction changes direction.

This equation is not a parabola so it has no vertex

ANSWER:

Translated 57 units upward

Vertical stretch

Reflection about the y-axis

Also, If the correct function is:

`f(x)=-10(x-5)^2+7`

Use the function:

`f(x)\text{ = a(}x-h)^2+k`

The parent function is:

`g(x)=x^2`

The transformations here are:

-5 indicates a horizontal shift of 5 units to the right

+7 indicates a vertical shift of 7 units upward

There was a reflection about the x-axis

The graph was vertically stretched

The vertex here is: (h, k) ==> (5, 7)