How do you find the vertex of a parabola $f (x) = x^{2} + 7 x + 6$ $f(x)=x^2+7x+6$ ?

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How do you find the vertex of a parabola $f (x) = x^{2} + 7 x + 6$ $f(x)=x^2+7x+6$ ?

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Answer 1 · 2015-07-08T19:34:35

The vertex is located at $(- \frac{7}{2}, - \frac{25}{4})$ $(-7/2,-25/4)$

Explanation:

Given $f (x) = x^{2} + 7 x + 6$ $f(x)=x^2+7x+6$

Complete the square
$XXXX$ $color(white)("XXXX")$ $= x^{2} + 7 x + {(\frac{7}{2})}^{2} - {(\frac{7}{2})}^{2} + 6$ $=x^2+7x +(7/2)^2 -(7/2)^2 +6$
Simplify into vertex form
$XXXX$ $color(white)("XXXX")$ $= {(x + \frac{7}{2})}^{2} - \frac{25}{4}$ $=(x+7/2)^2 -25/4$
or
$XXXX$ $color(white)("XXXX")$ $= {(x - (- \frac{7}{2}))}^{2} + (- \frac{25}{4})$ $=(x- (-7/2))^2+(-25/4)$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ which is the vertex form with vertex at $(- \frac{7}{2}, - \frac{25}{4})$ $(-7/2,-25/4)$

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How do you find the vertex of a parabola $f (x) = x^{2} + 7 x + 6$ $f(x)=x^2+7x+6$ ?

1 Answer

Explanation:

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How do you find the vertex of a parabola $f (x) = x^{2} + 7 x + 6$ $f(x)=x^2+7x+6$ ?