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How do you write the quadratic function in intercept form given x intercepts -2,2 and point (-4,8)?

Answer 1

Nathan Axel

#y=2/3(x^2-4)#

A quadratic equation in intercept form given #x# intercepts #-2,2# is

#y=a(x-(-2))(x-2)# or #y=a(x+2)(x-2)#

i.e. #y=a(x^2-4)#

As it passes through #(-4,8)#, we have

#8=a((-4)^2-4)# or #12a=8# or #a=8/12=2/3#

Hence, quadratic equation is #y=2/3(x^2-4)#

graph{(2/3(x^2-4)-y)((x+4)^2+(y-8)^2-0.04)=0 [-9.42, 10.58, -1.56, 8.44]}

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Answer 2

Eva Adamson

To write the quadratic function in intercept form given x-intercepts -2 and 2 and point (-4,8), first, find the quadratic equation using the x-intercepts:

( (x + 2)(x - 2) = 0 )

Expand and simplify:

( x^2 - 2x + 2x - 4 = 0 )

( x^2 - 4 = 0 )

( x^2 = 4 )

So, the quadratic equation in intercept form is ( y = (x + 2)(x - 2) ).

To find the quadratic function with the given point (-4,8), substitute the values of x and y into the equation:

( 8 = (-4 + 2)(-4 - 2) )

( 8 = (-2)(-6) )

( 8 = 12 )

This is not true, so there might be a mistake in the given information.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.