Question

A quadratic function has a line of symmetry at x=-3.5 and zero at -9 what is the distance from the given zero to line of symmetry

Answer 1

If a quadratic function has zero at x=-9, then point (-9,0) lies on the graph of quadratic function.

A line of symmetry has equation x=-3.5 that is x+3.5=0.

Use formula for the distance from point $(x_0,y_0)$ to the line AX+By+C=0:

$d=\dfrac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}}.$

Thus,

$d=\dfrac{|-9+3.5|}{\sqrt{1^2+0^2}}=5.5.$

Answer: the distance is 5.5 units.