Q24. Find the vertex and the x-intercept(s) (if any) and y-intercept for the quadratic function . Sketch the function.

Background

Topic: Quadratic Functions and Their Graphs

This question tests your understanding of quadratic functions in vertex form, how to find the vertex, x-intercepts, and y-intercepts, and how to sketch the graph.

Key Terms and Formulas:

• Vertex form:

• Vertex:

• X-intercepts: Solve

• Y-intercept:

Step-by-Step Guidance

1. Identify the vertex from the equation. In , and , so the vertex is .

2. To find the y-intercept, substitute into the function: .

3. To find the x-intercepts, set and solve for : .

4. Rearrange and solve for to find the x-intercepts.

Try solving on your own before revealing the answer!

Q25. Find the vertex, x-intercept(s), and y-intercept for the quadratic function . Sketch the function.

Background

Topic: Quadratic Functions in Standard Form

This question tests your ability to find the vertex, x-intercepts, and y-intercept for a quadratic function in standard form, and to sketch its graph.

Key Terms and Formulas:

• Standard form:

• Vertex:

• X-intercepts: Solve

• Y-intercept:

Step-by-Step Guidance

1. Find the vertex using . Here, , , so .

2. Plug this value into to find the coordinate of the vertex.

3. To find the y-intercept, substitute into the function: .

4. To find the x-intercepts, solve using factoring or the quadratic formula.

Try solving on your own before revealing the answer!