Which graph shows the quadratic function y 3x2 12x 10

Asked by maham237 @ 20/02/2021 in Mathematics viewed by 340 People

Which graph shows the quadratic function y = 3x2 − 12x + 10? (5 points)

Answered by maham237 @ 20/02/2021

ANSWER

The graph in option D.

EXPLANATION

The given function is:

$y = 3 {x}^{2} - 12x + 10$

We complete the square to obtain:

$y = 3( {x}^{2} - 4x) + 10$

$y = 3( {x}^{2} - 4x + {( - 2)}^{2} ) + 10 - 3 {( - 2)}^{2}$

$y = 3{( x- 2)}^{2}+ 10 - 12$

$y = 3{( x- 2)}^{2} - 2$

The graph of this function opens upwards and has its vertex at (2,-2).

The y-intercept is 10.

From the options the graph that satisfies all these properties is D.

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