graph the equation.\ny = 2(x - 4)^2+5

Explanation:

Step1: Identify the vertex form

The equation $y = 2(x - 4)^2+5$ is in vertex - form $y=a(x - h)^2 + k$, where $(h,k)$ is the vertex. Here, $h = 4$ and $k = 5$, so the vertex is $(4,5)$.

Step2: Determine the direction of the parabola

Since $a = 2>0$, the parabola opens upward.

Step3: Find additional points

Let's find the $y$ - value when $x = 3$. Substitute $x = 3$ into the equation: $y=2(3 - 4)^2+5=2\times(-1)^2+5=2 + 5=7$. Let's find the $y$ - value when $x = 5$. Substitute $x = 5$ into the equation: $y=2(5 - 4)^2+5=2\times1^2+5=2 + 5=7$. Plot the vertex $(4,5)$ and the points $(3,7)$ and $(5,7)$ and draw a smooth curve to graph the parabola.

Answer:

The graph is a parabola with vertex $(4,5)$ opening upward. Points $(3,7)$ and $(5,7)$ can be used to help draw the curve.