Question

given the parent graph $y = x^2$, write an equation of the quadratic parent function that has been
reflected over the x-axis
vertically stretched by a factor of 5
translated left 6 and up 1

Explanation:

Step1: Reflect over x-axis

Multiply parent function by -1: $y = -x^2$

Step2: Vertically stretch by 5

Multiply by stretch factor: $y = -5x^2$

Step3: Translate left 6

Replace $x$ with $x+6$: $y = -5(x+6)^2$

Step4: Translate up 1

Add 1 to the function: $y = -5(x+6)^2 + 1$

Answer:

$y = -5(x+6)^2 + 1$