Question

Graph the function. Identify the y-intercept, axis of symmetry, and vertex of the function. Does the vertex represent a maximum or minimum value? Create table if needed.

Answer 1

$\begin{gathered} f(x)=\text{ 2x}^2\text{ +4x - 6} \\ To\text{ find y-intercept is when x-value is 0. Then:} \\ \\ f(x)=\text{ 2\lparen0\rparen}^2\text{ + 4\lparen0\rparen - 6} \\ f(x)=\text{ -6} \\ \\ The\text{ y-intercept is \lparen0, -6\rparen} \\ \\ To\text{ find the axis of symmetry, is the vertical line:} \\ x=\text{ -}\frac{b}{2a},\text{ where a is 2 and b is 4.} \\ \\ x=\text{ -}\frac{4}{2(2)} \\ \\ x=\text{ - }\frac{4}{4} \\ x=\text{ -1} \\ \\ The\text{ vertex of the function is:} \\ h=\text{ - }\frac{b}{2a} \\ h=\frac{\text{ -4}}{2(2)}=\frac{\text{ -}4}{4}=\text{ -1} \\ \\ Now,\text{ we can replace the x for -1 to find k} \\ f(x)=2x^2+4x\text{ - }6 \\ f(\text{ -1\rparen=2\lparen-1\rparen}^2+4\text{ \lparen-1\rparen - 6} \\ f(\text{ -1\rparen=2\lparen1\rparen -4 -6} \\ f(\text{ -1\rparen=2-10} \\ f(\text{ -1\rparen = -8} \end{gathered}$

Then, the vertex is ( -1, -8)

If a is positive, in this case it is 2, then the parabola opens up, so the vertex is the minimumm value