How do you write $y = - 5 x^{2} + x + 1$ $y=-5x^2 +x +1$ in vertex form and identify the vertex, y intercept and x intercept?

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How do you write $y = - 5 x^{2} + x + 1$ $y=-5x^2 +x +1$ in vertex form and identify the vertex, y intercept and x intercept?

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Answer 1 · 2015-05-19T16:43:38

x of vertex: $x = (- \frac{b}{2} a) = \frac{- 1}{- 10} = \frac{1}{10}$ $x = (-b/2a) = (-1)/-10 = 1/10$

y of vertex: $y = f (\frac{1}{10}) = (- \frac{5}{100}) + \frac{1}{10} + 1 = \frac{105}{100}$ $y = f(1/10) = (-5/100) + 1/10 + 1 = 105/100$

Vertex form: $f (x) = - 5 {(x - \frac{1}{10})}^{2} + \frac{105}{100} .$ $f(x) = -5(x - 1/10)^2 + 105/100.$

Check by developing:

$f (x) = - 5 (x^{2} - \frac{2 x}{10} + \frac{1}{100}) - + \frac{105}{100}$ $f(x) = -5(x^2 - (2x)/10 + 1/100) -+ 105/100$
$= - 5 x^{2} + x - \frac{5}{100} + \frac{105}{100} = - 5 x^{2} + x + 1 .$ $= -5x^2 + x - 5/100 + 105/100 = -5x^2 + x + 1.$ OK

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How do you write $y = - 5 x^{2} + x + 1$ $y=-5x^2 +x +1$ in vertex form and identify the vertex, y intercept and x intercept?

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How do you write $y = - 5 x^{2} + x + 1$ $y=-5x^2 +x +1$ in vertex form and identify the vertex, y intercept and x intercept?