WRITING QUADRATIC EQUATION FROM GRAPHS 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

Problem 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

Problem 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

Problem 1 :

The roots of a quadratic equation are -2 and -6. The minimum point of the graph of its related function is at (-4, -2). Sketch the graph of the function.

Solution

Problem 2 :

The roots of a quadratic equation are -6 and 0. The minimum point of the graph of its related function is at (-3, 4). Sketch the graph of the function.

Solution

Problem 3 :

Which of the following x equations represent the parabola?

a)   y = 2(x − 2)(x + 1)    b) y = 2(x + 0.5)² − 4.5   c) y = 2(x − 0.5)² − 4.5

d) y = 2(x + 2)(x − 1)

Solution

Problem 4 :

 x-intercepts of 12 and −6; passes through (14, 4)

Solution

Problem 5 :

 x-intercepts of 9 and 1; passes through (0, −18)

Solution

Problem 6 :

x-intercepts of −16 and −2; passes through (−18, 72)

Solution

Problem 7 :

Describe and correct the error in writing an equation of the parabola.

Solution

Problem 1 :

Form the equation whose roots are 1 and -5.

Solution

Problem 2 :

Form the equation whose roots are

(√3 - 2)/2 and (√3 + 2)/2

Solution

Problem 3 :

If 1 – i and 1 + i are the roots of the equation

x² + ax + b = 0

where a, b ∈  r, then find the values of a and b.

Solution

Problem 4 :

The roots of a quadratic equation are -2 and -6. The minimum point of the graph of its related function is at (-4, -2). Sketch the graph of the function.

Solution

Problem 5 :

The roots of a quadratic equation are -6 and 0. The minimum point of the graph of its related function is at (-3, 4). Sketch the graph of the function.

Solution

Problem 6 :

Which equations have roots that are equivalent to the x-intercepts of the graph shown?

a) -x² - 6x - 8 = 0      b) 0 = (x + 2)(x + 4)     c)  0 = -(x + 2)² + 4

d) 2x² - 4x - 6 = 0      e) 4(x + 3)² - 4 = 0

Solution