Question

If the graph of the function g defined by g (r)-5x2 +3 is translated vertically upward by 7 units, it becomes the graph of a function /. Find the expression for h (r r)

Answer 1

When ever a function translate vertically upwards or down wards it means there is a constant quantity being added in the independent variable i.e.

When ever a function translate vertically upwards or down wards it means there is a constant quantity being added in the independent variable i.e. f(x) rightarrow f(x) + a Where a is the amount by which the graphs translate, if upwards, its positive, if downwards its negative So lets say a graph of ours i.e. g(x) = -5x^2 + 3 is translated to become h(x) And the translate is 7 units upwards means a = 7 So here we have- g(x) rightarrow^a h(x) = > h(x) = g(x) + 7 = > h(x) = -5x^2 + 3 + 7 = > h(x) = -5x^2 + 10 So the expression for h(x) is- h(x) = -5x^2 + 10 or h(x) = -5(x^2-2) (can be rewritten as this also if we take -5 common)

Where $\small a$ is the amount by which the graphs translate, if upwards, its positive, if downwards its negetive

So lets say a graph of ours i.e. is translated to become $\small h(x)$
And the translate is $\small 7$ units upwards means $\small a=7$

So here we have-
$\small g(x)\overset{a}{\rightarrow}h(x)$


$\small =>h(x)=-5x^2+10$

So the expression for $\small h(x)$ is-

or
(can be rewiritten as this also if we take $\small -5$ common)