# How do you find the vertex and intercepts for f(x)=4x^2-32x+63?

Dec 10, 2015

I have given the answer to and shown the method to obtain
$\textcolor{b l u e}{{x}_{\text{vertex}} = + 4}$
I have given the method to find the rest.

#### Explanation: color(blue)("To find " x_("vertex"))

Given: $y = 4 {x}^{2} - 32 x + 63 \ldots \ldots . . \left(1\right)$

Write as: $4 \left({x}^{2} - \frac{32}{4} x\right) + 63$

Consider the $- \frac{32}{4} \text{ from } - \frac{32}{4} x$

${x}_{\text{vertex}} = \left(- \frac{1}{2}\right) \left(- \frac{32}{4}\right) = + \frac{32}{8} = 4. . . \left(2\right)$
This compares to the graph
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$\textcolor{b r o w n}{\text{Method from this point:}}$

color(blue)("To find " y_("vertex"))

Substitute (2) into (1) to solve for ${y}_{\text{vertex}}$
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color(blue)("To find " y_("intercept"))

${y}_{\text{intercept}} = 63$ this is the constant at the end of equation (1)

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color(blue)("To find " x_("intercept"))

Substitute $y = 0$ in equation (1) and solve for $x$

If you are not sure about factoring use the formula

Standard form: $y = a {x}^{2} + b x + c$

where $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

You can see from the graph that your answers should be close to 3 1/2 " and " 4 1/2 color(red)(" "underline("These are estimates"))