Question

What is the vertex in the following function? y = 3(x + 5)^2 − 4

A. (5, -4)
B. (-5, -4)
C. (-15, -4)
D. (-5, 4)

Answer 1

`\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} y=a(x- h)^2+ k\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y=3(x+5)^2-4\implies y=3[x-\stackrel{h}{(-5)}]^2\stackrel{k}{-4}~\hfill \stackrel{vertex}{(-5,-4)}`

Answer 2

Add 4 to both sides

y + 4 = 3(x + 5)^2

Divide both sides by 3

y + 4/3 = (x + 5)^2

Rewrite in standard form;

(-5, -4)

Answer: B. (-5, -4)