91Ó°ÊÓ

If a parabola has two \(x\) -intercepts, explain how to find them.

The hypotenuse of a right triangle is 4 feet long. One leg is 1 foot longer than the other. Find the lengths of the legs. Round to the nearest tenth of a foot.

If 3 times a number is increased by 2 and this sum is squared, the result is \(49 .\) Find the number(s).

Write 0.00397 in scientific notation.

The distance, \(d,\) in feet, that an object falls in \(t\) seconds is modeled by the formula \(d=16 t^{2} .\) Use this formula to solve Exercises \(75-76\) If you drop a rock from a cliff 576 feet above the water, how long will it take for the rock to hit the water?

The radicand of the quadratic formula, \(b^{2}-4 a c,\) can be used to determine whether \(a x^{2}+b x+c=0\) has solutions that are rational, irrational, or not real numbers. Explain how this works. Is it possible to determine the kinds of answers that one will obtain to a quadratic equation without actually solving the equation? Explain.

Solve: $$x^{2}+2 \sqrt{3} x-9=0$$

A rectangular vegetable garden is 5 feet wide and 9 feet long. The garden is to be surrounded by a tile border of uniform width. If there are 40 square feet of tile for the border, how wide, to the nearest tenth of a foot, should it be?

What is the square root property?

Explain how to solve \((x-1)^{2}=16\) using the square root property.