Maths help???

(x + 4)(x - 2) = 0
x = - 4 , x = 2
(-4,0) and (2,0) are points on the x axis.

f(0) = - 8
(0,-8) is point on y axis.

(0,-8) is a Minimum turning point.

If x^2 + 2x - 8 = 0
(x+4) (x-2) = 0
x = -4 or 2

x^2 + 2x - 8 = 0
(x + 4)(x - 2) = 0

x + 4 = 0
x = -4

x - 2 = 0
x = 2

∴ x = -4 , 2

The question is specifically asking you to use the graph to solve the equation so calculations are not required.

Solving the equation means finding the values of x for which

x^2 + 2x - 8 = 0 is true.

That is the values of x when y = 0. Look at you graph ans see where it cuts the x axis. At these points y will = 0 and the two values of x are the solutions to the equation.

However, to help you I have solved the equation and without seeing the graph the solutions are x = -4 and x = 2

x² + 2x – 8 = 0
x²+ 4x – 2x – 8 = 0
x(x + 4) – 2(x + 4) = 0
(x – 2)(x + 4) = 0
(x – 2) = 0 or (x + 4) = 0
x = 2 or x = – 4

Determine where the graph of y=x^2+2x-8 intersects or crosses the x-axis.
That will give you the solutions to the equation x^2 +2x -8 = 0.

In general, if you have a function y=P(x), where P(x) is a polynomial, then the solutions to the equation P(x) = 0 are the points where the graph intersects or crosses the x-axis.

okay so using the x^2+2x-8=0, we can find the x intercepts :
(x+4)(x-2)=0 , x=-4,2 becasue
x+4=0
x=-4

x-2=0
x=2

Then from y=x^2+2x-8, the y intercept can be found by letting x=0; y=-8

All you need to do is look at the graph where y=0. If y=0 the 2 equations are the same.

As it;s a square graph there will be two answers where it crosses the x-axis (The answers should be -4 and 2).

x = 2 y = 0

(x+4)(x-2), so when when y is 0 x is -4 and 2, and seeing is x^2 positive, the curve is point down. (Simple quadratic)

when x=0 y=-8 (Blatantly obvious)

The use differentiation on x^2+2x-8 to get 2x+2, minimum when d2y/dx^2=0 so solve 2x+2=0 to get 2(x+1), therefore x=-1 at minimum, put that back in the original eqtn, you get (-1)^2+2(-1)-8 = -9, hence minimum occurs at (-1,-9)

Those points should be enough to draw a graph.

Wow... I had really out done myself LOL Haven't done maths for a few years now... I hope I am right... other people have probably answered it already, but hey, it's nice to have a bit of challenge everything now and again.

Hope this helps! Good luck with your studies. I am guessing you are doing GCSEs?