Download 93 Solving Quadratic Equations

9­3 Solving Quadratic Equations root​
(noun) root Related Words: ​
x­intercept, zero, solution Main Idea: ​
A root is a solution of an equation in the form f (x) = 0 . The related function y = f (x) has a ​
zero​
, and the graph of y = f (x) has an x­intercept, for each root of the equation. Example: ​
The equation x2 − 1 = 0 has two ​
roots​
. So, the function y = x2 − 1 has two ​
zeros​
: − 1 and 1 . Essential Understanding​
Quadratic equations can be solved by a variety of methods, including graphing and finding square roots. One way to solve a quadratic equation ax2 + bx + c = 0 is to graph the related quadratic functions y = ax2 + bx + c . The solutions of the equation are the x­intercepts of the related function. You can solve quadratic equations by a variety of methods. One way to solve a quadratic equation ax2 + bx + c = 0 is to graph the related quadratic function ax2 + bx + c = 0 . The solutions of the equation are the x­intercepts of the related function. A quadratic equation can have two, one, or no real­number solutions. In a future course you will learn about solutions of quadratic equations that are not real numbers. In this course, ​
solutions​
refers to real­number solutions. The solutions of a quadratic equation and the x­intercepts of the graph of the related function are often called ​
roots of the equation​
or ​
zeros of the function​
. solve each equation by graphing the related function. If the equation has no real­number solution, write no solution. A.) x2 + 7 = 0 B.) 3x2 − 12 = 0 2
C.) 31 x − 3 = 0 D.) x2 + 5 = 5 E.) x2 + 25 = 0 F.) 2x2 − 18 = 0 You can solve equations of the form x2 = k by finding the square roots of each side. For example, the solutions of x2 = 81 are ± √81 , or ± 9 . Solve each equation by finding square roots. If the equation has no real­number solution, write no solution. G.) a2 = 324
H.) r2 + 49 = 49
I.) 4g2 = 25 J.) 5q2 − 20 = 0
K.) 2r2 − 32 = 0
L.) 5z2 − 45 = 0 You can solve some quadratic equations that model real­world problems by finding square roots. In many cases, the negative square root may not be a reasonable solution. Model each problem with a quadratic equation. Then solve. If necessary, round to the nearest tenth. M.) find the length of a side of a square with an area of 75 ft2 . N.) ​
Painting​
You have enough paint to cover an area of 50 ft 2 . What is the side length of the largest square that you could paint? Round your answer to the nearest tenth of a foot.