How do you graph and label the vertex and axis of symmetry of $y = 3 (x - 1) (x - 4)$ $y=3(x-1)(x-4)$ ?

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Answer 1 · 2017-07-17T05:47:18

Vertex $(2.5, - 6.75)$ $(2.5, -6.75)$

Axis of Symmetry $x = 2.5$ $x=2.5$

Given -

$y = 3 (x - 1) (x - 4)$ $y=3(x-1)(x-4)$

Let us rewrite it as -

$y = (3 x - 3) (x - 4)$ $y=(3x-3)(x-4)$
$y = 3 x^{2} - 3 x - 12 x + 12$ $y=3x^2-3x-12x+12$
$y = 3 x^{2} - 15 x + 12$ $y=3x^2-15x+12$

Vertex -

$x = \frac{- b}{2 a} = \frac{- (- 15)}{2 \times 3} = \frac{15}{6} = \frac{5}{2}$ $x=(-b)/(2a)=(-(-15))/(2 xx 3)=15/6=5/2$

At $x = \frac{5}{2} = 2.5$ $x=5/2=2.5$

$y = 3 {(2.5)}^{2} - 15 (2.5) + 12$ $y=3(2.5)^2-15(2.5)+12$
$y = 18.75 - 37.5 + 12 = - 6.75$ $y=18.75-37.5+12=-6.75$

Vertex $(2.5, - 6.75)$ $(2.5, -6.75)$

Axis of Symmetry $x = 2.5$ $x=2.5$

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Take a few values on either side of $x = 2.5$ $x=2.5$
Find the corresponding y value. Tabulate them and plot them.

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How do you graph and label the vertex and axis of symmetry of y=3(x−1)(x−4)y=3(x-1)(x-4)?