Question

function g is a transformation of the parent function f(x)=x^2, The graph of g is a translation left 4 units down and down 2 units of the graph of f. Write the equation for g in the form y=ax^2+bx+c

Answer 1

To translate the graph of f left 4 units and down 2 units, we need to subtract 4 from the x-values and subtract 2 from the y-values of the points on the graph of f. So, the equation for g can be written as:

g(x) = (x - 4)^2 - 2

Expanding this equation, we get:

g(x) = x^2 - 8x + 16 - 2

Simplifying further:

g(x) = x^2 - 8x + 14

Therefore, the equation for g in the form y = ax^2 + bx + c is:

y = x^2 - 8x + 14