# Worksheet: Solving Quadratic Equations Graphically

In this worksheet, we will practice solving quadratic equations using function graphs.

Q1:

Consider the graph: The roots of a quadratic can be read from the graph. What are they?

• A1 and
• B and and
• C
• D and
• E and 1

Q2:

The diagram shows the graph of . What is the solution set of the equation ? • A
• B
• C
• D
• E

Q3:

If the graph of the quadratic function cuts the -axis at the points and , what is the solution set of in ?

• A
• B
• C
• D
• E

Q4:

Solve by factoring, and hence determine which of the following figures would be a sketch of .

• A • B • C • D • E Q5:

The graph shows the curve with equation . What is the solution set of the equation ? • A
• B
• C
• D

Q6:

If the point is the vertex of the graph of the quadratic function , what is the solution set of the equation ?

• A
• B
• C
• D

Q7:

The curve of a quadratic function, , intersects the -axis at the points and . What is the solution set of the equation ?

• A
• B
• C
• D
• E

Q8:

Consider the equation . In the following, find a solution by filling the blank space.

.

• A
• B
• C
• D
• E

.

• A
• B
• C
• D
• E

.

• A
• B
• C
• D
• E

.

• A
• B
• C
• D
• E

These solutions can be plotted as seen in the figure. What will be true of any other solution plotted in the plane? • AThey will not lie on the curve.
• BThey will not lie in the same quadrant.
• CThey will lie on the curve.
• DThey will lie on the -axis.
• EThey will lie in the same quadrant.

Q9:

Solve by factoring, and hence determine which of the following figures would be a sketch of .

• A • B • C • D • E Q10:

Consider the function .

Find the solutions when in the form of .

• A,
• B,
• C,
• D,
• E,

Find the solutions when in the form of .

• A,
• B,
• C,
• D,
• E,

Find the solutions when in the form of .

• A,
• B,
• C,
• D,
• E,

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution? • AThey will lie on the -axis.
• BThey will lie in the same quadrant.
• CThey will not lie on the curve.
• DThey will not lie in the same quadrant.
• EThey will lie on the curve.

Q11:

Work out the coordinates that satisfy the equation for the given values of .

.

• A,
• B,
• C,
• D,
• E,

.

• A,
• B,
• C,
• D,
• E,

.

• A,
• B,
• C,
• D,
• E,

.

• A
• B
• C
• D
• E

The solutions found can be plotted in plane as seen in the given figure. What will be true of the plot of any other solution? • AThey will not lie on the curve.
• BThey will not lie in the same quadrant.
• CThey will lie on the -axis.
• DThey will lie on the curve.
• EThey will lie in the same quadrant.

Q12:

Solve by factoring, and hence determine which of the following figures would be a sketch of .

• A • B • C • D • E Q13:

Using the given graph of the equation , find which of the following is the best approximation for the solutions to . • A or 2
• B or 1.5
• C or 1

Q14:

The graph shows the function . What is the solution set of ?

• A
• B
• C
• D
• E

What is the solution set of ?

• A
• B
• C
• D
• E

Q15:

The graph shows the function . What is the solution set of ? • A
• B
• C
• D
• E

Q16:

By drawing a graph of the function , find the solution set of .

• A
• B
• C
• D
• E