Question

Function A is a quadratic function with a vertex at (3, 4) and a leading coefficient of -1 Function B has the equation y = |x + 2|. Function A is then reflected over the x-axis and shifted down 2 while function B is reflected over the x-axis and shifted up 3. Which function has the larger y-intercept after being transformed and by how much?

Answer 1

With the information given, we deduce that the parabola is

$y=-(x-3)^2+4 = -(x^2-6x+9)+4 = -x^2+6x-5$

Reflecting a function over the x axis means to change its sign. After the reflection, the parabola becomes

$y=x^2-6x+5$

And to shift down a function, you subtract the shift from the equation: the equation becomes

$y=x^2-6x+5-2=x^2-6x+3$

Similarly, the other function is reflected over the x axis (sign change) and shifted up 3 (add 3 to the equation):

$|x+2|\mapsto -|x+2|\mapsto -|x+2|+3$

In order to compute the y intercept, we simply have to evaluate the functions at x=0: for the parabola we have

$y(0)=3$

For the other function, we have

$y(0)=-|2|+3=-2+3=1$