FINDING EQUATION OF QUADRATIC FUNCTION FROM GRAPH WORKSHEET

Determine the equation of quadratic function from graph. Give the function in general form.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Example 6 :

The area of a rectangle is modeled by the graph where y is the area (in square meters) and x is the width (in meters). Write an equation of the parabola. Find the dimensions and corresponding area of one possible rectangle. What dimensions result in the maximum area?

Solution

Example 7 :

Every rope has a safe working load. A rope should not be used to lift a weight greater than its safe working load. The table shows the safe working loads S (in pounds) for ropes with circumference C (in inches). Write an equation for the safe working load for a rope. Find the safe working load for a rope that has a circumference of 10 inches.

Solution

Determine the equation of quadratic function from graph. Give the function in vertex form.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Which function represents the widest parabola? Explain your reasoning.

a) y = 2(x + 3)²        b)  y = x² − 5     c)  y = 0.5(x − 1)² + 1      d)  y = −x² + 6

Solution

Problem 6 :

The graph of which function has the same axis of symmetry as the graph of

y = x² + 2x + 2?

a) y = 2x² + 2x + 2       b)  y = −3x²− 6x + 2

c)  y = x² − 2x + 2       d)  y = −5 x²+ 10x + 2

Solution

Problem 7 :

The path of a diver is modeled by the function

f(x) = −9x² + 9x + 1

where f(x) is the height of the diver (in meters) above the water and x is the horizontal distance (in meters) from the end of the diving board.

a. What is the height of the diving board?

b. What is the maximum height of the diver?

c. Describe where the diver is ascending and where the diver is descending.

Solution

Find the equation of each parabola.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Describe the transformation of the graph of the parent quadratic function. Then identify the vertex. 

f(x) = 2(x + 3)² + 2

Solution

Problem 8 :

write a rule for g described by the transformations of the graph of f. Then identify the vertex.

f(x) = x²

vertical stretch by a factor of 4 and a reflection in the x-axis, followed by a translation 2 units up

Solution

Problem 9 :

Match the function with its graph. Explain your reasoning.

a) g(x) = 2(x − 1)² − 2

b) g(x) = 1/2 ( x + 1)² − 2

c) g(x) = −2(x − 1)² + 2

d) g(x) = 2(x + 1)² + 2

e) g(x) = −2(x + 1)² − 2

f) g(x) = 2(x − 1)² + 2

Solution

Related Pages

• Find vertex and axis of symmetry of parabola from graph
• Formation of the quadratic equation from roots
• Determine equation of axis of symmetry
• Domain range axis of symmetry vertex and zeroes of quadratic function
• Finding maximum or minimum of quadratic function
• Graphing quadratic function in vertex form
• Determine if a function linear quadratic or constant
• Problems involving quadratic functions
• Equation of parabola from three points