Question

How do you find the x and y intercepts for `y = x^2 + 2x - 3`?

Answer 1

`" "`
x-intercepts are : `color(blue)((1,0), (-3,0)`

y-intercept: `color(blue)((0,-3)`

Explanation:

`" "`
Standard Form of a quadratic equation is `color(blue)(ax^2+bx+c=0`

We have a quadratic function `color(red)(y=f(x)=x^2+2x-3`

`color(green)("Step 1"`

x-intercepts is a point on the graph where `color(blue)(y=0`

Solve `color(red)(y=x^2+2x-3=0`

`rArr x^2+2x-3=0`

Split the middle term to find the factors.

`rArr x^2+3x-1x-3=0`

`rArr x(x+3)-1(x+3)=0`

`rArr (x+3)(x-1)=0`

`x+3 = 0 or x-1 =0`

`x=-3 or x=1`

Hence, x-intercepts are `(1,0), (-3,0)`

`color(green)("Step 2"`

y-intercepts is the point on the graph where `color(blue)(x=0`

Solve `color(red)(y=x^2+2x-3, "with x"= 0`

`rArr y = (0)^2+2(0)-3`

`:. y = -3`

Hence, y-intercept is at `(0,-3)`

You can verify these solutions by analyzing the quadratic graph: