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# Parabola

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The x intercepts of the parabola y=2x^2+13x-7-x^2-6x
are at (p,0)  and (q,0)  Find p and q

Enter your answer in the form "p, q ".

May 23, 2022

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To find the x-intercepts, we let y = 0 and solve for x. If x = a is a possible value of x, that corresponds to the x-intercept (a, 0).

But before that, we need to simplify it first.

$$y = 2x^2 +13x - 7 - x^2 - 6x \\y= x^2 + 7x - 7$$

Then let y = 0, and solve the equation using quadratic formula:

$$x^2 + 7x - 7 = 0\\ x= \dfrac{-7 \pm \sqrt{7^2 - 4(1)(-7)}}{2(1)}\\ x = \boxed{\phantom{\dfrac{-7 \pm \sqrt{7^2 - 4(1)(-7)}}{2(1)}}}$$

Each solution corresponds to one x-intercept, as I explained above.

May 23, 2022