Question

How do you find the vertex and axis of symmetry of `y = 3x^2 + 7x – 4`?

Answer 1

`color(blue)(x_("vertex")=-7/6)`
`color(blue)("Axis of symmetry "-> x=-7/6`
I will let you solve for `y_("vertex")` by substitution

Explanation:

Given:`" "y=3x^2+7x-4`

Write as:`" " y=3(x^2+7/3x)-4`

Consider the `7/3" from "7/3x`

Apply: `" "(-1/2)xx7/3 = -7/6`

`color(blue)(x_("vertex")=-7/6)`

`color(blue)("Axis of symmetry "-> x=-7/6`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute `color(red)(x=-7/6)` in the original equation to find `y_("vertex")`

`y_("vertex") = 3(color(red)(-7/6))^2 +7(color(red)(-7/6))-4`

I will let you finish this bit