Question

The axis of symmetry of a quadratic function has the equation x=4 if one zero is 7 ,what is the other zero ?

Answer 1

`x=1`

Explanation:

The axis of symmetry is central to the points where the graph crosses the x-axis (if there are any).

Axis of symmetry is `x=4`. So it is a line parallel to the y-axis and passes through the point `(x,y)=(4,0)`

The 7 is to the right of the axis of symmetry so the other x-intercept is to the left of it

Axis of symmetry to 7 is `7-4=color(red)(3)`

So the point to the left is `4-color(red)(3)=1`

Answer 2

To begin, a nice clue here is the axis of symmetry

Explanation:

The graphs of quadratic equations are known as parabolas and are symmetric everywhere.

Since your axis of symmetry is at x = 4, and there is a root at x = 7, that means the distance along x to one of the roots is 7 - 4 = 3.

Since this is a symmetric curve, that means your other root is at 4 - 3 = `1

So, your roots (zeros) are 7 and 1.

That makes your factors (x - 1) and (x - 7)

Then, to finish this equation fully (much farther than your problem asks), the quadratic equation is then found by FOIL multiplication

`(x-1)(x-7)->x^2-7x-1x+7->x^2-8x+7`