Write an equation for a function that has the graph with the shape of y=x​ squared but reflected across the​ y-axis and shifted left 7 units and up 5 unit.

Answer 1

y = x^2 is a parabola with vertex at the origin, (0,0)

reflected across the y axis changes nothing. It's still the same parabola, the same equation y=x^2

shifted left converts y=x^2 to y=(x+2)^2, with new vertex = (-2,0)

shifting up 5 changes the equation to y=(x+2)^2 + 5, with final vertex (-2, 5)

f(x) = (x+2)^2 + 5

or

f(x) = x^2 +4x + 9