We know what we have to find, so let's find it. **1. What are the intercepts?**
First, the *x*-intercepts. We need to find the roots of the quadratic polynomial. If we find them, we can celebrate by drinking a root beer. We need to find the solutions to the equation 0 = -*x*^{2} + 2*x* + 3 = -(*x*^{2} – 2*x* – 3). This equation factors as 0 = -(*x* – 3)(*x* + 1), so the solutions (and the *x*-intercepts) are *x* = 3, *x* = -1.
We can graph these points: The *y*-intercept is the constant term, 3, so we can graph that also: **2. What is the vertex?**
The vertex occurs halfway between the *x*-intercepts -1 and 3, so at *x* = 1. When we plug *x* = 1 in to the quadratic equation, we find -(1)^{2} + 2(1) + 3 = 4, so the vertex occurs at (1, 4). **3. Does the parabola open upwards or downwards?**
Since the coefficient on the *x*^{2} term is negative, the parabola opens downwards. Putting together all the pieces, we find our graph: We know this graphing stuff can be infectious, but be careful. We don't want you to get a graph infection. |