h(x)=x2+9x+18
Step 1 of 3: Find the vertex.


To find the vertex of the quadratic function \( h(x) = x^2 + 9x + 18 \), we can use the vertex formula for a parabola in the form \( ax^2 + bx + c \). The x-coordinate of the vertex is given by:

\[
x_{\text{vertex}} = -\frac{b}{2a}
\]

For the given function \( h(x) = x^2 + 9x + 18 \), we identify:
- \( a = 1 \)
- \( b = 9 \)

Now, substitute these values into the formula:

\[
x_{\text{vertex}} = -\frac{9}{2(1)} = -\frac{9}{2} = -4.5
\]

Next, to find the y-coordinate of the vertex, substitute \( x_{\text{vertex}} = -4.5 \) back into the original equation \( h(x) \):

\[
h(-4.5) = (-4.5)^2 + 9(-4.5) + 18
\]
\[
h(-4.5) = 20.25 - 40.5 + 18 = -2.25
\]

Thus, the vertex of the function is \( (-4.5, -2.25) \).

Would you like more details or have any questions about this?

Here are some related questions:
1. How do you find the axis of symmetry of a quadratic function?
2. What does the vertex tell us about the graph of the parabola?
3. How can you determine if the vertex is a maximum or a minimum?
4. Can you rewrite this quadratic function in vertex form?
5. How do the coefficients of a quadratic function affect its graph?

**Tip:** The vertex of a parabola is its turning point, which can either be the maximum or minimum depending on the direction the parabola opens.

h(x)=x^2+9x+18. Step 1 of 3: Find the vertex.

Learn how to find the vertex of the quadratic function h(x) = x^2 + 9x + 18 using the vertex formula. This step-by-step guide walks through calculating the vertex coordinates, ideal for students in Grades 9-10 studying quadratic functions.

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