Question

which is one of the transformations applied to the graph of $f(x)=x^2$ to produce the graph of $g(x)=2x^2 - 28x + 3$?

• shifted up 3 units
• shifted left 7 units
• shifted right 7 units
• shifted down 3 units

Explanation:

Step1: Factor out leading coefficient

$g(x)=2(x^2 - 14x) + 3$

Step2: Complete the square

$g(x)=2[(x^2 -14x + 49) - 49] + 3$

Step3: Simplify to vertex form

$g(x)=2(x - 7)^2 - 98 + 3 = 2(x - 7)^2 - 95$

Step4: Compare to parent function

For $f(x)=x^2$, $g(x)$ has horizontal shift: $x\to x-7$ means right 7 units.

Answer:

shifted right 7 units