Solution Bank Quadratic Functions Target E
Answers to the Practice Problems are below in random order.
\(\begin{align}&d=0;\ \text{1 real, rational}\ & \ \ \ \ &-4(2x-3)(x+1)\ & \ \ \ \ &d=-4;\ \text{2 complex}\\\\
&d=74;\ \text{2 real, irrational}\ & \ \ \ \ &d=81;\ \text{2 real, rational}\ & \ \ \ \ &x= \pm\frac{8}{9}\\\\
&\text{2 Real, 0 Complex}\ & \ \ \ \ &\text{0 Real, 2 Complex}\ & \ \ \ \ &\text{1 Real (Double Root), 0 Complex}\\\\
&61\ & \ \ \ \ &d=900;\ \text{2 real, rational}\ & \ \ \ \ &\text{1 real, rational x-intercept}\\\\
&\text{2 irrational x-intercepts}\ & \ \ \ \ &\text{no x-intercepts}\ & \ \ \ \ &\text{2 real, rational x-intercepts}\end{align}\)
\(\text{Vertex (-4,5) is above the x-axis and the graph opens down, so f(x) has two x-intercepts}\)
\(\text{Vertex (2,3) is above the x-axis and the graph opens up, so f(x) has no x-intercepts}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&d=0;\ \text{1 real, rational}\ & \ \ \ \ &-4(2x-3)(x+1)\ & \ \ \ \ &d=-4;\ \text{2 complex}\\\\
&d=74;\ \text{2 real, irrational}\ & \ \ \ \ &d=81;\ \text{2 real, rational}\ & \ \ \ \ &x= \pm\frac{8}{9}\\\\
&\text{2 Real, 0 Complex}\ & \ \ \ \ &\text{0 Real, 2 Complex}\ & \ \ \ \ &\text{1 Real (Double Root), 0 Complex}\\\\
&61\ & \ \ \ \ &d=900;\ \text{2 real, rational}\ & \ \ \ \ &\text{1 real, rational x-intercept}\\\\
&\text{2 irrational x-intercepts}\ & \ \ \ \ &\text{no x-intercepts}\ & \ \ \ \ &\text{2 real, rational x-intercepts}\end{align}\)
\(\text{Vertex (-4,5) is above the x-axis and the graph opens down, so f(x) has two x-intercepts}\)
\(\text{Vertex (2,3) is above the x-axis and the graph opens up, so f(x) has no x-intercepts}\)