the graph of h is the graph of f(x)=x^2 translated 4 units left and 7 units down. Write the function H in vertex form.

Answer:

f(x)=a(x - h)2 + k

Much like a linear function, k works like b in the slope-intercept formula. Like where add or subtract b would determine where the line crosses, in the linear, k determines the vertex of the parabola. If you're going to go up 2, then you need to add 2.

The h determines the movement horizontally. what you put in h determines if it moves left or right. To adjust this, you need to find the number to make the parentheses equal 0 when x equals -2 (because moving the vertex point to the left means subtraction/negatives):

x - h = 0

-2 - h = 0

-h = 2

h = -2

So the function ends up looking like:

f(x)=a(x - (-2))2 + 2

Subtracting a negative cancels the signs out to make a positive:

f(x)=a(x + 2)2 + 2

Step-by-step explanation:

The translated value of the function is h ( x ) = ( x + 4 )² - 7

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x²

we can obtain the function h(x) by first translating it 4 units to the left, which gives us f(x + 4), and then translating it 7 units down, which gives us f(x + 4) - 7. Therefore, the function h(x) can be written as:

h(x) = f(x + 4) - 7

To write this in vertex form, we need to complete the square. First, we have:

h(x) = f(x + 4) - 7

h(x) = (x + 4)² - 7

This is the vertex form of the equation for h(x). The vertex of the parabola is at the point (-4, -7), which is obtained by setting x + 4 = 0 in the equation above.

The value of the vertex is -7, which is obtained by subtracting 7 from the squared term.

Therefore, the vertex form of the equation for h(x) is:

h ( x ) = ( x + 4 )² - 7

Hence , the transformed function is h ( x ) = ( x + 4 )² - 7

To learn more about transformation of functions click :

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