Q4. Find the vertex and axis of symmetry of the graph of the function f(x) = x^2 + 10x.

Background

Topic: Quadratic Functions

This question is testing your understanding of how to find the vertex and axis of symmetry for a quadratic function in standard form. These are key features for graphing and analyzing parabolas.

Key Terms and Formulas:

• Vertex: The point where the parabola changes direction (minimum or maximum).

• Axis of Symmetry: A vertical line that divides the parabola into two symmetric halves.

• Standard form of a quadratic:

• Vertex formula:

• Axis of symmetry:

• To find the y-coordinate of the vertex, substitute the x-value back into the function.

Step-by-Step Guidance

1. Identify the coefficients: , , for .

2. Use the axis of symmetry formula: .

3. Plug in the values: .

4. Calculate the x-coordinate of the vertex (but do not finish the calculation yet).

5. To find the y-coordinate of the vertex, substitute the x-value into : .

Try solving on your own before revealing the answer!