Q1. For the quadratic function :

• a) Vertex: ____________

• b) _____, Parabola opens _________

• c) Axis of symmetry: ________________

• d) y-intercept: _____________________

• e) x-intercept(s): _________________

• f) Sketch the graph

Background

Topic: Quadratic Functions (Standard Form)

This question tests your understanding of the properties of quadratic functions, including how to find the vertex, axis of symmetry, intercepts, and how to sketch the graph of a parabola.

Key Terms and Formulas

• Standard form:

• Vertex: where and

• Axis of symmetry:

• y-intercept: Set and solve for

• x-intercepts: Set and solve for

• If , parabola opens upward; if , opens downward

Step-by-Step Guidance

1. Identify the coefficients: , , .

2. Find the vertex using :

3. Find the value by plugging back into :

4. State the axis of symmetry:

5. Find the y-intercept by evaluating :

6. Find the x-intercepts by solving (factor or use quadratic formula).

Try solving on your own before revealing the answer!

Q2. For the quadratic function :

• a) Vertex: ____________

• b) _____, Parabola opens _________

• c) Axis of symmetry: ________________

• d) y-intercept: _____________________

• e) x-intercept(s): _________________

• f) Sketch the graph

Background

Topic: Quadratic Functions (Standard Form)

This question is similar to Q1 but with a negative leading coefficient, which affects the direction the parabola opens.

Key Terms and Formulas

• Standard form:

• Vertex: where and

• Axis of symmetry:

• y-intercept: Set and solve for

• x-intercepts: Set and solve for

• If , parabola opens downward

Step-by-Step Guidance

1. Identify the coefficients: , , .

2. Find the vertex using :

3. Find by plugging into :

4. State the axis of symmetry:

5. Find the y-intercept by evaluating at :

6. Find the x-intercepts by solving (use quadratic formula if needed).

Try solving on your own before revealing the answer!

Q3. For the quadratic function :

• a) Vertex: ____________

• b) _____, Parabola opens _________

• c) Axis of symmetry: ________________

• d) y-intercept: _____________________

• e) x-intercept(s): _________________

• f) Sketch the graph

Background

Topic: Quadratic Functions (Vertex Form)

This question uses the vertex form of a quadratic function, which makes it easier to identify the vertex and axis of symmetry.

Key Terms and Formulas

• Vertex form:

• Vertex:

• Axis of symmetry:

• y-intercept: Set and solve for

• x-intercepts: Set and solve for

Step-by-Step Guidance

1. Identify , , and from the equation: , , .

2. State the vertex:

3. Axis of symmetry is

4. Find the y-intercept by evaluating :

5. Find the x-intercepts by solving

Try solving on your own before revealing the answer!

Q4. For the quadratic function :

• a) Vertex: ____________

• b) _____, Parabola opens _________

• c) Axis of symmetry: ________________

• d) y-intercept: _____________________

• e) x-intercept(s): _________________

• f) Sketch the graph

Background

Topic: Quadratic Functions (Vertex Form)

This question involves a quadratic in vertex form with a negative leading coefficient, affecting the direction of the parabola.

Key Terms and Formulas

• Vertex form:

• Vertex: (note: means )

• Axis of symmetry:

• y-intercept: Set and solve for

• x-intercepts: Set and solve for

Step-by-Step Guidance

1. Identify , , and from the equation: , , .

2. State the vertex:

3. Axis of symmetry is

4. Find the y-intercept by evaluating at :

5. Find the x-intercepts by solving

Try solving on your own before revealing the answer!

Q5. For the quadratic function :

• a) Vertex: ____________

• b) _____, Parabola opens _________

• c) Axis of symmetry: ________________

• d) y-intercept: _____________________

• e) x-intercept(s): _________________

• f) Sketch the graph

Background

Topic: Quadratic Functions (Vertex Form)

This question uses the vertex form, making it straightforward to identify the vertex and axis of symmetry.

Key Terms and Formulas

• Vertex form:

• Vertex:

• Axis of symmetry:

• y-intercept: Set and solve for

• x-intercepts: Set and solve for

Step-by-Step Guidance

1. Identify , , and from the equation: , , .

2. State the vertex:

3. Axis of symmetry is

4. Find the y-intercept by evaluating at :

5. Find the x-intercepts by solving

Try solving on your own before revealing the answer!