How do you find parabola equation given vertex is (2,3) and the zeros are x=0 and x=4?

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How do you find parabola equation given vertex is (2,3) and the zeros are x=0 and x=4?

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Answer 1 · 2018-06-30T12:59:06

$y = - \frac{3}{4} x^{2} + 3 x$ $y=-3/4x^2+3x$

Explanation:

$using the intercept form$ $"using the "color(blue)"intercept form"$

$∙ x y = k (x - a) (x - b)$ $•color(white)(x)y=k(x-a)(x-b)$

$where a and b are the zeros and k is a multiplier$ $"where a and b are the zeros and k is a multiplier"$

$y = k (x - 0) (x - 4) = k x (x - 4)$ $"y=k(x-0)(x-4)=kx(x-4)$

$to find k substitute (2, 3) into the equation$ $"to find k substitute "(2,3)" into the equation"$

$3 = 2 k (- 2) \Rightarrow - 4 k = 3 \Rightarrow k = - \frac{3}{4}$ $3=2k(-2)rArr-4k=3rArrk=-3/4$

$y = - \frac{3}{4} x (x - 4) = - \frac{3}{4} x^{2} + 3 x$ $y=-3/4x(x-4)=-3/4x^2+3x$
graph{-3/4x^2+3x [-10, 10, -5, 5]}

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How do you find parabola equation given vertex is (2,3) and the zeros are x=0 and x=4?

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