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

1 Answer
Apr 20, 2018

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

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

Explanation:

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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:

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