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How do you writer this function in standard form??

How do you writer this function in standard form??-example-1
User Robrtc
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Question 1) Function defining the table:

From the table the x-intercepts are -2 and 1. This means the factors are:

(x+2) and (x-1)

Let


h(x) = a(x + 2)(x - 1)

The point (-1,-1) satisfy this function since it is from the same table.


- 1 = a( - 1 + 2)( - 1 - 1) \\ - 1 = - 2a \\ a = (1)/(2)

Therefore the function is


h(x) = (1)/(2) (x + 2)(x - 1)

We expand to get:


h(x) = (1)/(2) ( {x}^(2) + x - 2)

The standard form is:


h(x) = \frac{ {x}^(2) }{2} + (x)/(2) - 1

Question 3) Parabola opening up

The x-intercepts are x=3 and x=7

The factors are (x-3), (x-7)

The factored from is


y = a(x - 3)(x - 7)

The curve passes through (5,-4)


- 4= a( 5- 3)( 5 - 7) \\ - 4= - 4a \\ a = 1

The equation is:


y = (x - 3)(x + 7)

Expand:


y = {x}^(2) + 7x - 3x - 21


y = {x}^(2) + 4x - 21

This is the standard form:

Question 3) Parabola opening down:

The x-intercepts are x=-5 and x=1

The factors are (x+5), (x-1)

The factored form is


y = - (x + 5)(x - 1)

We expand to get:


y = - ( {x}^(2) - x + 5x - 5)


y = - {x}^(2) - 4x + 5

This is the standard form.

User Activelearner
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