Question

Could somebody please help me with some graphing in math?

"Consider the graphed quadratic function with one point located at point P. Plot a point on the graph that has integer coordinates and represents an average rate of change of 5 with point P."

Thank you for helping me out!

Answer 1

Q(-2,-7)

See attachment

Explanation:

We need to form a simultaneous equation and solve.

The point P has coordinates (1,8). Let the other point Q also have coordinate (x,y).

Then the average rate of change is the slope of the secant line connecting P(1,8) and Q(x,y) and this has a value of 5.

`\implies (8-y)/(1-x)=5`

`\implies 8-y=5(1-x)`

`\implies y=5x-3...(1)`

This point Q also lies on the given parabola whose equation is
`y=-(x-2)^2+9...(2)`

Put equation (1) into (2) to get:

`5x+3=-(x-2)^2+9`

`5x+3=-(x^2-4x+4)+9`

`5x+3=-x^2+4x-4+9`

`5x+3=-x^2+4x+5`

`x^2+x-2=0`

`(x-1)(x+2)=0`

`x=1,x=-2`

When x=-2, y=5(-2)-3=-7

Therefore the required point is Q(-2,-7)