WeBWorK using host: https://webwork.pcc.edu, format: simple, seed: 4397, course: orcca

Determine whether the graph of each quadratic function opens upward or downward.

The graph of the quadratic function $y=3x^2-4x-7$ opens .

The graph of the quadratic function $y=-5x^2+x$ opens .

The graph of the quadratic function $y=2+3x-x^2$ opens .

The graph of the quadratic function $y=\frac{1}{3}x^2-\frac{2}{5}x+\frac{1}{4}$ opens .

Solution

The graph of the quadratic function $y=3x^2-4x-7$ opens upward as the leading coefficient is the positive number $3\text{.}$

The graph of the quadratic function $y=-5x^2+x$ opens downward as the leading coefficient is the negative number $-5\text{.}$

The graph of the quadratic function $y=2+3x-x^2$ opens downward as the leading coefficient is $-1\text{.}$ (Note that the leading coefficient is the coefficient on $x^2\text{.}$ )

The graph of the quadratic function $y=\frac{1}{3}x^2-\frac{2}{5}x+\frac{1}{4}$ opens upward as the leading coefficient is the positive number $\frac{1}{3}\text{.}$