Which of these quadratic functions would produce a parabola that opens downward? A f(x)=16x^2+11x+8 B f(x)=2x^2+5x-3 B f(x)=-4x^2+2x+5 C D f(x)=0x^2-8x-3 D

## Step 1<br />The given problem is about quadratic functions and their graphical representation. A quadratic function is generally represented in the form \(f(x) = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants. The determines the direction of the parabola. If \(a > 0\), the parabola opens upwards, and if \(a < 0\), the parabola opens downwards.<br /><br />## Step 2<br />Let's analyze each option:<br /><br />### Option A: \(f(x) = 16x^2 + 11x + 8\)<br />Here, \(a = 16\), which is greater than 0. Therefore, the parabola opens upwards.<br /><br />### Option B: \(f(x) = 2x^2 + 5x - 3\)<br />Here, \(a = 2\), which is greater than 0. Therefore, the parabola opens upwards.<br /><br />### Option C: \(f(x) = -4x^2 + 2x + 5\)<br />Here, \(a = -4\), which is less than 0abola opens downwards.<br /><br />### Option D: \(f(x) = 0x^2 - 8x - 3\)<br />Here, \(a = 0\), which means the function is linear, not quadratic. Therefore, it does not represent a parabola.