Chapter 8

Graph each quadratic function, and state its domain and range. $$y=-\frac{1}{3} x^{2}+5$$

Solve each equation by using the quadratic formula. $$\frac{1}{3} t^{2}-t+\frac{1}{6}=0$$

Graph each quadratic function, and state its domain and range. $$y=-\frac{1}{2} x^{2}+3$$

Solve each equation by using the quadratic formula. $$\frac{3}{4} x^{2}-2 x+\frac{1}{2}=0$$

Graph each quadratic function, and state its domain and range. $$h(x)=(x-2)^{2}$$

Solve each equation by using the quadratic formula. $$2 t^{2}-6 t+5=0$$

Graph each quadratic function, and state its domain and range. $$h(x)=(x+3)^{2}$$

Solve each equation by using the quadratic formula. $$2 y^{2}+1=2 y$$

Find the vertex for the graph of each quadratic function. $$f(x)=x^{2}-9$$

Solve each equation by using the quadratic formula. $$-2 x^{2}+3 x=6$$

Find the vertex for the graph of each quadratic function. $$f(x)=x^{2}+12$$

Solve each equation by using the quadratic formula. $$-3 x^{2}-2 x-5=0$$

Find the vertex for the graph of each quadratic function. $$y=x^{2}-4 x+1$$

Solve each equation by using the quadratic formula. $$\frac{1}{2} x^{2}+13=5 x$$

Find the vertex for the graph of each quadratic function. $$y=x^{2}+8 x-3$$

Solve each equation by using the quadratic formula. $$\frac{1}{4} x^{2}+\frac{17}{4}=2 x$$

Find the vertex for the graph of each quadratic function. $$f(x)=-2 x^{2}+20 x+1$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$x^{2}-6 x+2=0$$

Find the vertex for the graph of each quadratic function. $$f(x)=-3 x^{2}+18 x-7$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$x^{2}+6 x+9=0$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$-2 x^{2}+5 x-6=0$$

Find the vertex for the graph of each quadratic function. $$y=x^{2}-x+1$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$-x^{2}+3 x-4=0$$

Find the vertex for the graph of each quadratic function. $$y=3 x^{2}-2 x+1$$

Find all intercepts for the graph of each quadratic function. $$f(x)=16-x^{2}$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$v^{2}=3 v+5$$

Find all intercepts for the graph of each quadratic function. $$f(x)=x^{2}-9$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$y^{2}-\frac{1}{2} y+\frac{1}{4}=0$$

Find all intercepts for the graph of each quadratic function. $$y=x^{2}-2 x-8$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$\frac{1}{2} w^{2}-\frac{1}{3} w+\frac{1}{4}=0$$

Find all intercepts for the graph of each quadratic function. $$y=x^{2}-x-6$$

Find all intercepts for the graph of each quadratic function. $$f(x)=-4 x^{2}+12 x-9$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$9-24 z+16 z^{2}=0$$

Find all intercepts for the graph of each quadratic function. $$f(x)=-2 x^{2}-x+3$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$9-24 z+16 z^{2}=0$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$f(x)=x^{2}-x-2$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$12-7 x+x^{2}=0$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$f(x)=x^{2}+2 x-3$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$g(x)=x^{2}+2 x-8$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$-6 x^{2}-5=0$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$g(x)=x^{2}+x-6$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$x^{2}=x$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$y=-x^{2}-4 x-3$$

Find \(b^{2}-4 a c\) and the number of real solutions to each equation. $$-3 x^{2}+7 x=0$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$y=-x^{2}-5 x-4$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$h(x)=-x^{2}+3 x+4$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$h(x)=-x^{2}-2 x+8$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$a=b^{2}-6 b-16$$

Find the vertex and intercepts for each quadratic function. Sketch the graph, and state the domain and range. $$v=-u^{2}-8 u+9$$

Find the maximum or minimum value of \(y\) for each function. $$y=x^{2}-8$$