A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line o

Question

Natalija

21 day ago

9

A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line o

f symmetry? What is the other zero of the quadratic function?

Mathematics

1 answer:

Svet_ta [9.5K] · Answer 1 · 2026-03-06T23:22:47+03:00

Given:

A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.

To find:

The second root.

Solution:

It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.

This implies that the line of symmetry passes through the midpoint of the two roots.

Let the other root be denoted as x.

$-3.5=\dfrac{(-9)+x}{2}$

Multiply both sides by 2.

$-7=-9+x$

Add 9 to both sides.

$-7+9=-9+x+9$

$2=x$

Consequently, the other zero of the quadratic function is concluded to be 2.