Question

The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?

Answer 1

a = 2

Explanation:

We know that the line of symmetry is equal to -b/2a. Since we know this, we can set up an equation by plugging in certain values.

The line of symmetry equals 2 and the line of symmetry equals -b/2a. By transitivity, 2 equals -b/2a.

In our equation, we are given what b is. b would be the second term in our quadratic equation, which is -8.

Now, we set up our equation and plug in known values.

2 = -b/2a

2 =
`-(-8)/(2a)`

Negatives cancel each other out:

2 =
`(8)/(2a)`

You can solve this part in many different ways, but I will do it using proportions:

`(2)/(1) = (8)/(2a)`

2a *2 = 8 * 1

4a = 8

Divide by 4 on both sides

a = 2

Let me know if you have any questions.