Mathematics: The image of the point (-1, -1)(under a translation is (4, 4)( Find the coordinates of the image of the point (-6, 5) under the same translation.

The image of the point (-1, -1)(under a translation

sweetLips230

28.03.2022

A. f(t)=4(t-1)^2+3 ; the minimum height of the roller coaster is 3 meters from the ground.

Step-by-step explanation:

The given function is,

f(t) = 4t^2 - 8t + 7

As the leading coefficient is 4 which is positive, so the parabola will open upward and at the vertex the value of the function will be minimum.

f(t)=4t^2-8t+7

=4(t^2-2t)+7

$=4(t^2-2\cdot t\cdot 1+1^2-1^2)+7$

$=4(t^2-2\cdot t\cdot 1+1^2-1)+7$

$=4(t^2-2\cdot t\cdot 1+1^2)-4+7$

$=4(t^2-2\cdot t\cdot 1+1^2)+3$

=4(t-1)^2+3

So the vertex form will be,

f(t)=4(t-1)^2+3

Hence the vertex will be at (1,3)

At vertex the value of the function ot f(t) is 3, so the minimum height of the roller coaster is 3 meters from the ground.

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