If the graph of y = (x - 2)^2 - 3 is translated 5 units up and 2 units to the right, then the equation of the graph obtained is given by
A. y = x^2 + 2
B. y = (x - 2)^2 + 5
C. y = (x + 2)^2 + 2
D. y = (x - 4)^2 + 2

Let f(x) = x^2 + 2x + 4. Which of the following statements is NOT true?
A. f(x) has a maximum value
B. The graph of f is not a line
C. The graph of f has no x-intercepts.
D. The graph of f has a y-intercept.

A translation is a movement of the graph either horizontally parallel to the axis or vertically parallel to the axis. To move a graph right, we add a negative value to the x-value. To move a graph left, we add a positive value to the x-value.

According to the question

1> The graph of y = [tex](x - 2)^2 - 3[/tex]

translation 5 units up and 2 units to the right

Now,

translation 5 units up that means we have to add +5 to move it up

i.e

y = [tex](x - 2)^2 - 3[/tex] + 5

y = [tex](x - 2)^2 +2[/tex]

Then

translation 2 units to the right

as per translation rules:

To move a graph right, we add a negative value to the x-value. To move a graph left, we add a positive value to the x-value.

i.e

y = [tex](x - 2-2)^2 +2[/tex]

y = [tex](x - 4)^2 +2[/tex]

2>The equation f(x) = [tex]x^2 + 2x + 4[/tex]

Analyzing all the options

Option A : f(x) has a maximum value

This statement is not true as y or f(x) can not be always max or min for all values of (x) .

Option B: The graph of f is not a line

This is true as it is a quadratic equations its graph will be parabola .

Option C: The graph of f has no x-intercepts

This statement is true as x intercepts means y = 0

but it cannot be possible

Option D: The graph of f has a y-intercept.

This statement is true as y intercepts means x = 0

at x= 0

the equation will be

f(x) = [tex]x^2 + 2x + 4[/tex]

f(x) = [tex]4[/tex]

Hence, The the equation of the graph obtained is y = [tex](x - 4)^2 +2[/tex] and the NOT true statement is f(x) has a maximum value .

To know more about translation in graph here:

https://brainly.com/question/11805053

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