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

Feb 23, 2018

$x = 1$

#### 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 $\left(x , y\right) = \left(4 , 0\right)$

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 $7 - 4 = \textcolor{red}{3}$

So the point to the left is $4 - \textcolor{red}{3} = 1$

Feb 23, 2018

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

$\left(x - 1\right) \left(x - 7\right) \to {x}^{2} - 7 x - 1 x + 7 \to {x}^{2} - 8 x + 7$