which equation represents a graph with a vertex at (-3, 2)?\n○ y = 4x² + 24x + 38\n○ y = 4x² - 24x + 38\n○ y…

which equation represents a graph with a vertex at (-3, 2)?\n○ y = 4x² + 24x + 38\n○ y = 4x² - 24x + 38\n○ y = 4x² + 12x + 2\n○ y = 4x² + 16x + 13

which equation represents a graph with a vertex at (-3, 2)?\n○ y = 4x² + 24x + 38\n○ y = 4x² - 24x + 38\n○ y = 4x² + 12x + 2\n○ y = 4x² + 16x + 13

Answer

Explanation:

Step1: Use the vertex form of a quadratic equation

The vertex form of a quadratic equation is (y = a(x - h)^2 + k), where ((h,k)) is the vertex. Here (h=-3), (k = 2) and (a = 4) (since the coefficient of (x^{2}) in all options is (4)). So (y=4(x+ 3)^{2}+2).

Step2: Expand the vertex - form equation

Expand (y = 4(x + 3)^{2}+2). First, ((x + 3)^{2}=x^{2}+6x + 9). Then (y=4(x^{2}+6x + 9)+2). [ \begin{align*} y&=4x^{2}+24x+36 + 2\ y&=4x^{2}+24x+38 \end{align*} ]

Answer:

(y = 4x^{2}+24x + 38) (the first option)