What is the solutions to y equals x2-x-12?

Answer 1

14

Answer 2

There are an infinite number of values that can be given for x and y to fit this equation. If you're looking to find out where it intercepts the x-axis, you can do so by solving for y = 0:

x2 - x - 12 = 0

(x - 4)(x + 3) = 0

x ∈ {-3, 4}

If you want to solve for when it intercepts the y-axis, then let x = 0:

y = 02 - 0 - 12

y = -12

If you want to find it's vertex, then you can do this a couple of ways. One would be to find it's derivative and solve for 0:

dy/dx = 2x - 1

0 = 2x - 1

2x = 1

x = 0.5

Now plug that back into the original equation to get the y co-ordinate:

y = 2(0.5) - 0.5 - 12

y = 1 - 0.5 - 12

y = -11.5

So the vertex is at the point (0.5, 11.5).