Question #c5316

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Question #c5316

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Answer 1 · 2017-10-01T09:16:46

$(2, 11), x = 2$ $(2,11),x=2$

Explanation:

$given the equation of a parabola in standard form$ $"given the equation of a parabola in standard form"$

$∙ x y = a x^{2} + b x + c x; a \neq 0$ $•color(white)(x)y=ax^2+bx+c color(white)(x);a!=0$

$then the x-coordinate of the vertex which is also the$ $"then the x-coordinate of the vertex which is also the"$
$axis of symmetry is$ $"axis of symmetry is"$

$x_{vertex} = - \frac{b}{2 a}$ $x_(color(red)"vertex")=-b/(2a)$

$f (x) = - x^{2} + 4 x + 7 is in standard form$ $f(x)=-x^2+4x+7" is in standard form"$

$with a = - 1, b = 4, c = 7$ $"with "a=-1,b=4,c=7$

$\Rightarrow x_{vertex} = - \frac{4}{- 2} = 2$ $rArrx_(color(red)"vertex")=-4/(-2)=2$

$substitute this value into the equation for y-coordinate$ $"substitute this value into the equation for y-coordinate"$

$\Rightarrow y_{vertex} = - 4 + 8 + 7 = 11$ $rArry_(color(red)"vertex")=-4+8+7=11$

$\Rightarrow vertex = (2, 11)$ $rArrcolor(magenta)"vertex "=(2,11)$

$axis of symmetry is x = 2$ $"axis of symmetry is "x=2$

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Question #c5316

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