Question

7. The parabola shown has the form y = ax2 + bx + c.

a. What is the axis of symmetry? x=
b. Look at the width of the parabola to find a.
c. Use the formula x = to find b.
2a
d. What is the equation of the parabola?

Answer 1

Answer: y = ax2 + bx + c

Explanation:

Step 1: The equation of any parabola is given by y = ax2 + bx + c, where a, b, and c are constants.

Step 2: We can calculate the axis of symmetry (x-coordinate) by using the formula x = -b/2a.

Step 3: We can calculate the value of a by looking at the width of the parabola.

Step 4: Once we have the values of a and b, we can substitute them into the equation to get the equation of the parabola: y = ax2 + bx + c.

Answer 2

The axis of symmetry is x = -1

The width is 1

The value of b is 2

The equation of the parabola is y = x² + 2x - 3

What is the axis of symmetry?

From the question, we have the following parameters that can be used in our computation:

The graph

The axis of symmetry is the line that divides the function to 2

So, we have

x = -1

Also, the width of the parabola is 1

Finding b, we have

x = -b/2a

So, we have

-1 = -b/2

This gives

b = 2

The equation of the parabola is

y = a(x - h)² + k

So, we have

y = a(x + 1)² - 4

Also, we have

a(-2 + 1)² - 4 = -2

a(-2 + 1)² = 2

a = 1

So, we have

y = (x + 1)² - 4

y = x² + 2x + 1 - 4

y = x² + 2x - 3

Hence, the equation of the parabola is y = x² + 2x - 3