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

Mar 7, 2016

$\textcolor{b l u e}{{x}_{\text{vertex}} = - \frac{7}{6}}$
color(blue)("Axis of symmetry "-> x=-7/6
I will let you solve for ${y}_{\text{vertex}}$ by substitution

#### Explanation:

Given:$\text{ } y = 3 {x}^{2} + 7 x - 4$

Write as:$\text{ } y = 3 \left({x}^{2} + \frac{7}{3} x\right) - 4$

Consider the $\frac{7}{3} \text{ from } \frac{7}{3} x$

Apply: $\text{ } \left(- \frac{1}{2}\right) \times \frac{7}{3} = - \frac{7}{6}$

$\textcolor{b l u e}{{x}_{\text{vertex}} = - \frac{7}{6}}$

color(blue)("Axis of symmetry "-> x=-7/6
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Substitute $\textcolor{red}{x = - \frac{7}{6}}$ in the original equation to find ${y}_{\text{vertex}}$

${y}_{\text{vertex}} = 3 {\left(\textcolor{red}{- \frac{7}{6}}\right)}^{2} + 7 \left(\textcolor{red}{- \frac{7}{6}}\right) - 4$

I will let you finish this bit