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

The midpoint of the segment PQ is (4, 8), and the equation of the line of symmetry for the quadratic curve y=x² - 8x + 15 is x = 4.

Step-by-step explanation:

To calculate the coordinates of the midpoint of the straight line segment PQ, we use the midpoint formula which involves averaging the x-coordinates and the y-coordinates of the two points.

Since P has coordinates (1, 8) and Q has coordinates (7, 8),

the midpoint M will have coordinates ((1+7)/2, (8+8)/2) which is (4, 8).

The quadratic curve is given by y = x² - 8x + 15.

The equation of the line of symmetry for a parabola of the form y = ax² + bx + c is x = -b/(2a).

For this quadratic, a = 1 and b = -8,

so the line of symmetry is x = 8/(2*1),

which simplifies to x = 4.

Answer 2

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.

Step-by-step 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=((x_1+x_2)/(2),(y_1+y_2)/(2)) \\ =((1+7)/(2),(8+8)/(2)) \\ =((8)/(2),(16)/(2)) \\ =(4,8) \end{gathered}`

Also, the equation of line PQ is,

`\begin{gathered} (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1) \\ (y-8)/(8-8)=(x-1)/(7-1) \\ (y-8)/(0)=(x-1)/(6) \\ y-8=0 \\ y=8 \end{gathered}`

Therefore,

The equation of the symmetry is, x=4.