Question

Points P and Q are on the quadratic curve y=x^2 - 8x + 15Calculate the coordinates of the midpoint of the straight libe segment PQ P(1,8) Q(7,8)Write down the equation of the line of symmetry for y=x^2 - 8x + 15

Answer 1

Given

The curve, y=x^2 - 8x + 15.

And, the points, P(1,8) and Q(7,8).

To find:

The midpoint of PQ, and the axis of symetry for y=x^2 - 8x + 15.

Explanation:

It is given that,

The curve, y=x^2 - 8x + 15.

And, the points, P(1,8) and Q(7,8).

That implies,

The midpoint of PQ is,

$\begin{gathered} Midpoint\text{ }of\text{ }PQ=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ =(\frac{1+7}{2},\frac{8+8}{2}) \\ =(\frac{8}{2},\frac{16}{2}) \\ =(4,8) \end{gathered}$

Also, the equation of line PQ is,

$\begin{gathered} \frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1} \\ \frac{y-8}{8-8}=\frac{x-1}{7-1} \\ \frac{y-8}{0}=\frac{x-1}{6} \\ y-8=0 \\ y=8 \end{gathered}$

Therefore,

The equation of the symmetry is, x=4.