Question

Determine if y=2(x−3)^2+6
a function by graphing

Answer 1

To determine if y=2(x−3)^2+6 is a function by graphing, we need to examine if it passes the vertical line test.

First, let's rewrite the equation in standard form:
y = 2(x^2 - 6x + 9) + 6
y = 2x^2 - 12x + 18 + 6
y = 2x^2 - 12x + 24

Now, let's graph the equation.

When we graph y = 2x^2 - 12x + 24, we get a parabola that opens upward.

Using the graph, we can see that for every x-coordinate, there is only one y-coordinate. Therefore, y=2(x−3)^2+6 is indeed a function.

Here is the graph:

{{graph(400,400,-2,8,-5,30,2x^2-12x+24)}}