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 $.