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

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Answer 1 · 2016-03-25T03:04:26

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: $(2,7)$ .

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