91Ó°ÊÓ

Why is the vertical line that passes through the vertex of a parabola called the axis of symmetry?

Explain how to use the product property of radicals to simplify \(\sqrt{3} \cdot \sqrt{15}\)

Evaluate the expression. $$-\sqrt{0.04}$$

Simplify the expression. $$\sqrt{44}$$

Evaluate the radical expression when \(a=2\) and \(b=4\). $$\frac{10 \pm 2 \sqrt{b}}{a}$$

Find the \(x\) -intercepts of the graph of the equation. $$y=2 x^{2}+4 x-30$$

If you double the height from which the object falls, do you double the falling time? If not, why?

You see a firefighter aim a fire hose from 4 feet above the ground at a window that is 26 feet above the ground. The equation \(h=-0.01 d^{2}+1.06 d+4\) models the path of the water when \(h\) equals height in feet. Estimate, to the nearest whole number, the possible horizontal distances \(d\) (in feet) between the firefighter and the building.

In Exercises 25 and 26 , use the vertical motion model \(\boldsymbol{h}=-\mathbf{1 6 t}^{2}+\boldsymbol{v t}+\boldsymbol{s}(\mathbf{p} . \mathbf{5 3 5})\) and the following information. You and a friend are playing basketball. You can jump with an initial velocity of 12 feet per second. You need to jump 2.2 feet to dunk a basketball. Your friend can jump with an initial velocity of 14 feet per second. Your friend needs to jump 3.4 feet to dunk a basketball. Can you dunk the ball? Can your friend? Justify your answers.

MULTI-STEP PROBLEM You are on a team that is building a roller coaster. The vertical height of the first hill of the roller coaster is supposed to be 220 feet. According to the design, the path of the first hill can be modeled by \(y=0.039 x^{2}-0.331 x+1.850,\) where \(y\) is the vertical height in feet and \(x\) is the horizontal distance in feet. The first hill can use only 75 feet of horizontal distance. a. Use the model to determine whether the first hill will reach a height of 220 feet. b. What minimum horizontal distance is needed for the first hill to reach a vertical height of 220 feet? c. Writing Can you build the first hill high enough? Explain your findings. d. CRITICAL THINKING Is the shape of the graph the same as the shape of the hill? Why or why not?