SOLUTION: Consider the following function f(x)=-4x^2-8x-3 a. Describe the transformation we would apply to the basic function g(x)=x^2, to obtain f. b. Give the vertex and axis of s

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Consider the following function f(x)=-4x^2-8x-3 a. Describe the transformation we would apply to the basic function g(x)=x^2, to obtain f. b. Give the vertex and axis of s      Log On


   

Question 949254: Consider the following function
f(x)=-4x^2-8x-3
a. Describe the transformation we would apply to the basic function g(x)=x^2, to obtain f.
b. Give the vertex and axis of symmetry.

My answer after graphing it.
a. The graph of a f(x)=-4x^2-8x-3 is a reflection in the x axis, a horizontal shift of 1 unit to the left, and a vertical shift of 1 unit upward of the graph of g(x)=x^2
The graph of a f(x)=-4x^2-8x-3 is a vertical stretch of the graph of g(x)=x^2 by a factor of 4.
b. The vertex is (-1,1) and the axis of symmetry is -1.
This doesn't look right and asking for assistance. Thanks.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f is in general form and g is in either standard or general form. Put f into standard form to determine the transformation to change g into f.

Complete the Square for f(x).
-4%28x%5E2%2B2x%2B3%2F4%29
-4%28x%5E2%2B2x%2B1%2B3%2F4-1%29
-4%28%28x%2B1%29%5E2%2B4%2F4-3%2F4%29

Continue putting into standard form.
-4%28%28x%2B1%29%5E2%2B1%2F4%29
-4%28x%2B1%29%5E2%2B1

Moving or changing g would go like this:
Reflect in the x-axis,
Multiply by 4,
Move 1 unit up,
Move 1 unit to the left.

#b is correct. I believe #a is also correct.