Question

How do you use the graph to solve `0=x^2+2x-7`?

Answer 1

`color(blue)((-1, -8)` & `color(red)((-7, 0)`

Explanation:

graph{x^2+2x-7 [-8.93, 8.85, -8.49, 0.4]}

`x=(-b)/(2a)`

`=(-2)/(2*1)`

`=>x=color(blue)(-1`

And, `y=x^2+2x-7`
`=(-1)^2+2(-1)-7`
`=>y=color(blue)(-8`

Therefore, the minimum point is `color(blue)((-1, -8)`.

To find the `y`-intercept, `x=0`
`(0)^2+2(0)-7`
`=color(red)(-7`

Therefore another solution is `color(red)((-7, 0)`.

Its zeroes will be its `x`-intercepts. So,

`x=((-b)+-sqrt(b^2-4ac))/(2a)`... Quadratic Formula

`x=((-2)+-sqrt(2^2-4*1*(-7)))/(2*1)`

`x=(-2+-sqrt(32))/2`

`x=color(orange)(-1+2sqrt(2)` OR `color(blue)(-1-2sqrt(2)`