Plot the points on the graph of f(x)=2(x-4)^2+4 that correspond to x-values of 2 and 3.

Question

Plot the points on the graph of f(x)=2(x-4)^2+4 that correspond to x-values of 2 and 3. Then plot the vertex and the reflections of these points in the axis of symmetry.

Answer 1

The vertex form of a quadratic is f(x) = a(x - h)² + k, where the vertex is the opposite of h, k stays the same.

So your vertex will be (4, 4)

Now to get the y values for your given x values, plug them in

f(x) = 2(x - 4)² + 4

2: f(2) = 2(2 - 4)² + 4 = 12. (2,12)

3: f(3) = 2(3 - 4)² + 4 = 6. (3, 6)

Since quadratics have symmetry, 2 and 3 are next to 4. So 5 and 6 will be the reflection points

(5, 6) and (6,12)