How do you find the vertex and intercepts for #y = x^2 - 4x + 12#?

Answer 1

Vertex is at #(2,8)#, y- intercept is #y=12 # or at #(0,12)# ,
x-intercept is absent.

#y=x^2-4x+12 or y= x^2-4x+4+8 # or
#y= (x-2)^2 + 8#, Comparing with standard equation of vertex
form, # y= a(x-h)^2+k ; (h,k)# being vertex , we find here
#h=2 , k =8#. So vertex is at #(2,8)#. y-intercept can be found by
putting #x=0# in the equation #y=x^2-4x+12 :. y = 12#
y- intercept is #y=12 # or at #(0,12)# . x-intercept can be found by
putting #y=0# in the equation #y=x^2-4x+12# or
#x^2-4x+12=0 ;(ax^2+bx+c=0) a=1 , b=-4 ,c=12 #
Discriminant #D= b^2-4ac= 16-48=-32 :. D<0# .
Since #D<0# the roots are complex in nature , so there is no

x-intercept. x-intercept is absent.

graph{x^2-4x+12 [-40, 40, -20, 20]} [Ans]

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Answer 2

To find the vertex of the parabola represented by the equation y = x^2 - 4x + 12, use the formula x = -b / (2a), where a = coefficient of x^2 term, and b = coefficient of x term. Substitute the values of a and b into the formula to find the x-coordinate of the vertex. Then, substitute this value back into the original equation to find the corresponding y-coordinate. To find the x-intercepts, set y = 0 and solve for x. To find the y-intercept, plug in x = 0 into the equation.

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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.

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.

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.

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.

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