Questions: Determine the vertex of the graph of the following parabola. f(x)=3(x-3)^2+4 Give your answer as an ordered pair (h, k).

Transcript text: Determine the vertex of the graph of the following parabola. \[ f(x)=3(x-3)^{2}+4 \] Give your answer as an ordered pair $(h, k)$.

Solution

Solution Steps

Step 1: Determine the x-coordinate of the vertex

To find the x-coordinate of the vertex, we use the formula $h = -\frac{b}{2a}$. Substituting the given values, we get $h = -\frac{-18}{2(3)} = 3$.

Step 2: Determine the y-coordinate of the vertex

To find the y-coordinate of the vertex, we substitute $h$ back into the original equation $f(x) = ax^2 + bx + c$. Thus, $k = a(h)^2 + b(h) + c = 3(3)^2 - 18(3) + 31 = 4$.

Final Answer:

The vertex of the parabola described by the equation $f(x) = 3x^2 - 18x + 31$ is at the point $(3, 4)$.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!