What is the axis of symmetry and vertex for the graph # y = -x^2 +4x + 3#?

Answer 1

We are going to use the expression to find the vertex of a parabola.

First of all, let us graph the curve:

graph{-x^2+4x+3 [-10, 10, -10, 10]}

This curve is a parabola, because of the form of its equation:

#y ~ x^2#
To find the vertex of a parabola, #(x_v, y_v)#, we must solve the expression:
#x_v= -b/{2a}#
where #a# and #b# are the coefficients of #x^2# and #x#, if we write parabola as it follows:
#y = ax^2+ bx + c#

So, in our case:

#x_v = - 4/{2*(-1)} = 2#
This gives us the axis of the parabola: #x=2# is the axis of symmetry.
Now, let us calculate the value of #y_v# by substituting #x_v# on parabola expression:
#y_v= - x_v^2 + 4 x_v + 3 = - 2^2+4 cdot 2 + 3 = 7#
So vertex is: #(2,7)#.
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Answer 2

Axis of symmetry: ( x = \frac{-b}{2a} = \frac{-4}{2(-1)} = 2 )

Vertex: To find the vertex, substitute the value of ( x ) into the equation:

( y = -x^2 + 4x + 3 ) ( y = -(2)^2 + 4(2) + 3 ) ( y = -4 + 8 + 3 ) ( y = 7 )

So, the vertex is ( (2, 7) ).

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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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