A parabola intersects the x-axis at x=3 and x=9. What is the x-coordinate of the parabola's vertex?

Identify Parabola Roots: The x-coordinates where the parabola intersects the x-axis are the roots of the parabola. For a parabola in standard form, y = ax^2 + bx + c, the x-coordinate of the vertex can be found using the formula -b/(2a). However, we do not have the coefficients a, b, and c. Instead, we can use the fact that the vertex of a parabola is exactly in the middle of the two x-intercepts for a vertical parabola.Calculate Vertex X-coordinate: Calculate the midpoint between the two x-intercepts to find the x-coordinate of the vertex. The midpoint formula is (x1 + x2) / 2, where x1 and x2 are the x-intercepts.Find Midpoint: Substitute the given x-intercepts into the midpoint formula: (3 + 9) / 2.Perform Calculation: Perform the calculation: (3 + 9) / 2 = 12 / 2 = 6.

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A parabola intersects the
x-axis at
x=3 and
x=9.
What is the
x-coordinate of the parabola's vertex?

A parabola intersects the $x$ -axis at $x=3$ and $x=9$ . $\newline$ What is the $x$ -coordinate of the parabola's vertex?

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Algebra 2

Rational functions: asymptotes and excluded values

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Q. A parabola intersects the

x

-axis at

x=3

and

x=9

\newline

What is the

x

-coordinate of the parabola's vertex?

Identify Parabola Roots: The $x$ -coordinates where the parabola intersects the $x$ -axis are the roots of the parabola. For a parabola in standard form, $y = ax^2 + bx + c$ , the $x$ -coordinate of the vertex can be found using the formula $-\frac{b}{2a}$ . However, we do not have the coefficients $a$ , $b$ , and $c$ . Instead, we can use the fact that the vertex of a parabola is exactly in the middle of the two $x$ -intercepts for a vertical parabola.
Calculate Vertex X-coordinate: Calculate the midpoint between the two x-intercepts to find the x-coordinate of the vertex. The midpoint formula is $(x_1 + x_2) / 2$ , where $x_1$ and $x_2$ are the x-intercepts.
Find Midpoint: Substitute the given x-intercepts into the midpoint formula: $(3 + 9) / 2$ .
Perform Calculation: Perform the calculation: $(3 + 9) / 2 = 12 / 2 = 6$ .