Question

Directions: write an appropriate equation for the given graph using your knowledge of parent functions and (h,k)

Answer 1

The parent functions are defined with all coefficients with value 1.

They can be linear, quadratic, cubic, absolute, reciprocal, exponential, logarithmic, square root, sine, cosine, tangent...

Then we can pick a function and transform it in order to include the point (-1,5) in the function definition.

We will use the quadratic parent function:

$y=x^2$

We will adjust the coefficient a of the quadratic function in order to include (-1,5)

$\begin{gathered} y=a\cdot x^2 \\ 5=a(-1)^2=a \\ a=5 \end{gathered}$

Then, our transformed function is:

$y=5a^2$