Questions: In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=3(x-7)^2-2 The vertex is - (Type an ordered pair.)

In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function.
f(x)=3(x-7)^2-2

The vertex is - (Type an ordered pair.)

Transcript text: Michael Painter Homework 10 Question 1, 3.1.9 HW Score: $0 \%, 0$ of 23 points Points: 0 of 1 Save In the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function. \[ f(x)=3(x-7)^{2}-2 \] The vertex is $\square$ - (Type an ordered pair.)

Solution

Solution Steps

Step 1: Understanding the Problem

Given a quadratic function in the form $f(x) = a(x-h)^2 + k$, where $a \neq 0$, the task is to find the vertex of the parabola described by this function. The parameters of the function are:

$a$: A non-zero coefficient affecting the parabola's width and direction.
$h$: The x-coordinate of the vertex.
$k$: The y-coordinate of the vertex. The vertex of the parabola is directly given by the ordered pair $(h, k)$.

Step 2: Applying the Solution Approach

Given the parameters:

$a = 3$
$h = 7$
$k = -2$ The vertex of the parabola can be found directly without any further calculations, as it is given by the parameters $(h, k)$ of the quadratic function.