Math Problem Statement
h(x)=x2+9x+18 Step 1 of 3: Find the vertex.
Solution
To find the vertex of the quadratic function , we can use the vertex formula for a parabola in the form . The x-coordinate of the vertex is given by:
For the given function , we identify:
Now, substitute these values into the formula:
Next, to find the y-coordinate of the vertex, substitute back into the original equation :
Thus, the vertex of the function is .
Would you like more details or have any questions about this?
Here are some related questions:
- How do you find the axis of symmetry of a quadratic function?
- What does the vertex tell us about the graph of the parabola?
- How can you determine if the vertex is a maximum or a minimum?
- Can you rewrite this quadratic function in vertex form?
- 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.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Functions
Vertex of a Parabola
Formulas
x_vertex = -b/2a
h(x) = ax^2 + bx + c
Theorems
Vertex formula for quadratic functions
Suitable Grade Level
Grades 9-10