91Ó°ÊÓ

How can we determine the number of \(x\) -intercepts of the graph of a quadratic function without graphing the function?

For the quadratic function \(f(x)=a(x-h)^{2}+k,\) in what quadrant is the vertex if the values of \(h\) and \(k\) are as follows? (a) \(h>0, k>0\) (b) \(h>0, k<0\) (c) \(h<0, k>0\) (d) \(h<0, k<0\) Consider the value of \(a\), and make the correct choice. (e) If \(a>0,\) then the graph opens (up / down). (f) If \(a<0\), then the graph opens (up / down). (g) If \(|a|>1\), then the graph is (narrower / wider) than the graph of \(f(x)=x^{2}\). (h) If \(0<|a|<1\), then the graph is (narrower \(/\) wider ) than the graph of \(f(x)=x^{2}\)

If the vertex of the graph of a quadratic function is \((1,-3),\) and the graph opens down, how many \(x\) -intercepts does the graph have?

Graph each absolute value function. \(f(x)=|x-1|\)

Find the vertex of each parabola. For each equation, decide whether the graph opens up, down, to the left, or to the right, and whether it is wider, narrower, or the same shape as the graph of \(y=x^{2} .\) If it is a parabola with a vertical axis of symmetry, find the discriminant and use it to determine the number of \(x\) -intercepts. f(x)=2 x^{2}+4 x+5

Plot each point, and then use the same axes to plot the points that are symmetric to the given point with respect to the following: (a) \(x\) -axis, (b) y-axis, (c) origin. $$ (-4,-2) $$

Graph each absolute value function. \(y=3|x-2|-1\)

Graph each absolute value function. \(y=\frac{1}{2}|x+3|+1\)

Graph each parabola. Give the vertex, axis of symmetry, domain, and range. \(f(x)=x^{2}+4 x+3\)

Graph each piecewise linear function. \(f(x)=\left\\{\begin{array}{ll}5 x-4 & \text { if } x \geq 1 \\ x & \text { if } x<1\end{array}\right.\)