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How do you write the Vertex form equation of the parabola # y=x^2+4x+1#?

Answer 1

Eli Assouline

# y = (x+2)^2 - 3

the standard form of a quadratic is #y = ax^2 + bx + c#

the equation here # y = x^2 + 4x + 1 #

provides, for example: a = 1, b = 4, and c = 1.

The equation's vertex form is

# y =a (x - h )^2 + k #

where the vertex's coords are (h, k).

x-coord of vertex = # -b/(2a) = -4/2 = -2 #

and y-coord # = (-2)^2 +4(-2) + 1 = 4 - 8 + 1 = -3#

Consequently, a = 1 and (h, k) = (-2, -3).

equation in vertex form is : # y = (x + 2)^2 - 3 #

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Answer 2

Kennedy Adams

The vertex form of a parabola equation is y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. To write the given quadratic equation y = x^2 + 4x + 1 in vertex form, complete the square on the quadratic term. Then, rewrite the equation in the form y = a(x - h)^2 + k.

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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.