Question

Could somebody please help me with some graphing in math?

Answer 1

Answer:

Q(-2,-7)

See attachment

Step-by-step 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.

$\implies \frac{8-y}{1-x}=5$

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

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

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)