Question

Write each relation in standard form and then find the y-intercept for each relation:

a) y = 5(x+10)^2 +7

Answer 1

In standard form, the relation is
`y = 5x^2 + 100x + 507`

The y-intercept is y = 507.

Explanation:

Quadratic equation:

In standard form, it is written as:

`y = ax^2 + bx + c`

The y-intercept is c.

a) y = 5(x+10)^2 +7

We open the binomial to write in standard form. So

`y = 5(x + 10)^2 + 7`

`y = 5(x^2 + 20x + 100) + 7`

`y = 5x^2 + 100x + 500 + 7`

`y = 5x^2 + 100x + 507`

In standard form, the relation is
`y = 5x^2 + 100x + 507`

The independent term, c, is 507, so the y-intercept is y = 507.