Given the function f(x)=5x^2+10x-15 convert it to vertex and factored form, and list the key properties of the function, and then graph it (graph paper on next page) [16]

## Step 1: Convert to Vertex Form<br />### To convert the quadratic function $f(x) = 5x^2 + 10x - 15$ into vertex form, we complete the square. The vertex form is given by $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex of the parabola. Here, $a = 5$, $b = 10$, and $c = -15$. The vertex $(h, k)$ can be found using $h = -\frac{b}{2a}$ and $k = f(h)$. Calculating these gives $h = -1.0$ and $k = -20.0$. Thus, the vertex form is $f(x) = 5(x - (-1.0))^2 + (-20.0)$.<br /><br />## Step 2: Convert to Factored Form<br />### To convert the function to factored form, we use the quadratic formula to find the roots (x-intercepts). The discriminant $D = b^2 - 4ac = 400$. The roots are $x_1 = \frac{-b + \sqrt{D}}{2a} = 1.0$ and $x_2 = \frac{-b - \sqrt{D}}{2a} = -3.0$. Therefore, the factored form is $f(x) = 5(x - 1.0)(x - (-3.0))$.<br /><br />## Step 3: List Key Properties<br />### The key properties of the function are:<br />- **Vertex**: $(-1.0, -20.0)$<br />- **Axis of Symmetry**: $x = -1.0$<br />- **X-Intercepts**: $(1.0, 0)$ and $(-3.0, 0)$<br />- **Y-Intercept**: $f(0) = -15$