WITHOUT a calculator, identify VERTEX form, GENERAL form, AND FACTORED FORM. Then use the three forms to write the vertex, $y$-intercept, AND $x$-intercepts of the function as prompted. \[ y=2(x+4)^{2}-8 \] Vertex Form: $y=$ General Form: $y=$ Factored Form: $y=$ x-intercept(s): $y$-intercept: Vertex: $(-4,-8)$ Question Help: $\square$ Video D Post to forum Submit Question Jump to Answer
Solution
Step 1 ：The given equation is already in the vertex form which is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex of the parabola. Here, $a=2$, $h=-4$ and $k=-8$.
Step 2 ：To find the general form, we need to expand the equation. The general form of the equation is $y=2x^{2}+16x+24$.
Step 3 ：The factored form can be found by setting the equation to zero and solving for $x$. The factored form of the equation is $y=(x+6)(x+2)$.
Step 4 ：The x-intercepts of the function are the values of $x$ for which $y=0$. The x-intercepts of the function are $x=-6$ and $x=-2$.
Step 5 ：The y-intercept of the function is the value of $y$ when $x=0$. The y-intercept of the function is $y=24$.
Step 6 ：The vertex of the function is given as $(-4,-8)$.
Step 7 ：Final Answer: \[\boxed{\begin{align*} \text{Vertex Form: } & y=2(x+4)^{2}-8, \text{General Form: } & y=2x^{2}+16x+24, \text{Factored Form: } & y=(x+6)(x+2), \text{x-intercept(s): } & x=-6, x=-2, \text{y-intercept: } & y=24, \text{Vertex: } & (-4,-8) \end{align*}}\]
