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How do you find the VERTEX of a parabola #y=x^2+7x+12#?

Answer 1

Nathan Axel

Use the method of completing the square to convert to vertex form and get the vertex at #(-7/2, -1/4)#

With the vertex at #(a,b)#, the vertex form is #y=m(x-a)^2+b#.

#y=x^2+7x+12#

y = x^2 + 7x + (7/2)^2 + 12 - (7/2)^2#

#rarr y = (48/4 - 49/4)# + (x+7/2)^2

y = (x-(-7/2))^2 + (-1/4)# #rarr

This is the vertex form with the vertex at #(-7/2,-1/4)#, #color(white)("XXXXXX")#.

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Answer 2

Eli Assouline

To find the vertex of a parabola in the form y = ax^2 + bx + c, use the formula x = -b / (2a). Then substitute the value of x into the equation to find the corresponding y-coordinate. For the given equation y = x^2 + 7x + 12, the vertex is (-7/2, 25/4).

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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.