Questions: What does the variable h represent in the Vertex Form of a parabola: f(x)=(x-h)^2+k ? The value of x at the x-intercept The value of x at the vertex The value of y at the y-intercept The value of y at the vertex The steepness of the slope

What does the variable h represent in the Vertex Form of a parabola: f(x)=(x-h)^2+k ?
The value of x at the x-intercept
The value of x at the vertex
The value of y at the y-intercept
The value of y at the vertex
The steepness of the slope

Transcript text: What does the variable h represent in the Vertex Form of a parabola: $f(x)=(x-h)^{2}+k$ ? The value of $x$ at the $x$-intercept The value of $x$ at the vertex The value of $y$ at the $y$-intercept The value of $y$ at the vertex The steepness of the slope

Solution

Solution Steps

Step 1: Identify the Vertex Form of a Parabola

The vertex form of a parabola is given by the equation:

$f(x) = (x-h)^2 + k$

In this form, the variables $h$ and $k$ represent specific characteristics of the parabola.

Step 2: Determine the Role of

h

In the vertex form, the variable $h$ represents the $x$ -coordinate of the vertex of the parabola. The vertex of the parabola is the point $(h, k)$ .

Step 3: Analyze the Multiple-Choice Options

Let's analyze the given options to determine which one correctly describes the role of $h$ :

The value of $x$ at the $x$ -intercept: This is incorrect because $h$ is not related to the $x$ -intercept.
The value of $x$ at the vertex: This is correct because $h$ is the $x$ -coordinate of the vertex.
The value of $y$ at the $y$ -intercept: This is incorrect because $h$ is not related to the $y$ -intercept.
The value of $y$ at the vertex: This is incorrect because $k$ represents the $y$ -coordinate of the vertex.
The steepness of the slope: This is incorrect because the steepness is not determined by $h$ .