Question

The parent function of a quadratic, f(x) =x is reflected across the

x-axis, vertically stretched by a factor of 10 and translated 3 units right
and 7 units down. Write the equation of the transformed quadratic
function, g(x), in vertex form.

Answer 1

To transform the parent function of a quadratic into the desired function, we reflect it across the x-axis, vertically stretch it, and translate it horizontally and vertically.

Step-by-step explanation:

The parent function of a quadratic is f(x) = x. To reflect the function across the x-axis, we change the sign of the function so it becomes f(x) = -x. To vertically stretch the function by a factor of 10, we multiply the function by 10, resulting in g(x) = -10x. To translate the function 3 units to the right, we subtract 3 from x, giving us g(x) = -10(x - 3). Finally, to translate the function 7 units down, we subtract 7 from the whole function, giving us g(x) = -10(x - 3) - 7.