What is the x intercepts of the curve y=-x^2 + 3x +18 ?.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the curve y= -x^2 + 3x +18

We need to find the x intercepts for y.

The x-intercepts are the values where the function meets the x-axis.

Then the values of y= 0

Let us substitute with y= 0 into the equation.

==> -x^2 + 3x +18 = 0

==> Multiply by -1.

==> x^2 - 3x -18 =0

Now we will factor.

==> (x-6)(x+3) = 0

==> x1= 6

==> x2= -3

Then the x-intercepts are the points ( 6,0) and (-3,0).

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

At the x-intercepts of the curve y = -x^2 + 3x + 18, the value of y = 0.

So we get 0 = -x^2 + 3x + 18

=> x^2 - 3x - 18 = 0

=> x^2 - 6x + 3x - 18 = 0

=> x(x - 6) + 3(x - 6) = 0

=> (x + 3)(x - 6) = 0

=> x = -3 and x = 6

The required intercepts of y = -x^2 + 3x + 18 with the x-axis are (-3 , 0) and (6, 0)

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