Math PT

 Solving quadratic equation by using the square root method Example 1: Solve x² = 27 Step 1:  get the square root of both sides  √x^2 = ± √27 Step 2:  since 27 doesn't have a square root we find its perfect square x = ± √9 • 3 Step 3:  Once you find its perfect square factor it x = ± √9  √3 Step 4:  get the square root of the perfect square Answer: x = ± 9√3 Example 2: solve 2(y - 8)² = 50 Step 1:  divide both sides by 2 √(y - 8)² = ± √25 Step 2:  get the square root of both sides y - 8 = + -5 Step 3:  since  5 may be + or - we have 2 equations y - 8 = 5  add 8 + 5 y = 13 y - 8 = -5 subtract 8 - 5 y = 3 the roots of the equation are: 13 and 3

Steps in how to solve quadratic equations and getting their graphs Graph of f(x) = x² + k Example 1: g(x) = x² + 3 Step 1: To graph the example, we'll need a given table of values, so we will make one. g(x)  -3/ -2/ -1/ 0/ 1/ 2/ 3/ Step 2: Then after, we will replace x with the given numbers and solve. g(-3) = (-3)² + 3 g(-3) = 9 + 3 g(-3) = 12 g(-2) = (-2)² + 3 g(-2) = 4 + 3 g(-2) = 7 g(-1) = (-1)² + 3 g(-1) = 1 + 3 g(-1) = 4 g(0) = (0)² + 3 g(0) = 3 g(1) = (1)² + 3 g(1) = 1 + 3 g(1) = 4 g(2) = (2)² + 3 g(2) = 4 + 3 g(2) = 7 g(3) = (3)² + 3 g(3) = 9 + 3 g(3) = 12 g(x)  x   -3/12 -2/7 -1/4 0/3 1/4 2/7 3/12 Step 3: Then, after solving and finishing the table of values, we will graph. Graph of g(x) = x² Example 2: g(x) = x² Step 1: To graph g(x) = x² , you will need a table of values, so let's make one. g(x) x -3/ -2/ -1/ 0/ 1/ 2/ 3/ Then, we'll replace x with the given and multiply/raise it to the power of 2 . g(-3) = (-3)² (-3)² = 9 -3² = 9 g(-2) = (-2)² (-2)² = 4 -...

  Solving quadratic equations using quadratic formula Example 1 Step 1:  First we bring the equation in the form of ax² + bx+ c = 0 . 2x² - 14 + 24 = 0 Step 2:  then we list the coefficients a, b, and c a = 2  b = -14 c = 14 Step 3:  then we plug these coefficients in the formula of (-b ± √(b² - 4ac)/(2a) . x= - (-14) ± √(-14)² - 4(2)(14) (2)(2) Step 4:  then, we raise -14 to the power of 2 which is 196 . Then we multiply -4 with positive two and multiply the answer with positive 14 . And we also multiply 2 with 2 . x = - (-14 ± √(196 - 192) (4) Step 5:  then, we shall subtract 196 with 192 . x = 14 ± √(4)    (4) Step 6:  after subtracting, we shall get the square root of 4 . x = 14 ± 2        (4) Then, we shall get the solution. Step 7:  first, we add 14 with positive 2 and copy the denominator. Then we divide the denominator with the answer to 14 plus positive 2 .    x = 14 + 2   ...

Steps in how to solve a quadratic equation using factoring Example no. 1:  x ² + 6x + 5 = 0 Step 1 : To factorize the equation x ² + 9x + 8 = 0 , we need to break down the quadratic term ( 9x ) into two terms whose coefficients multiply to give 8 and add up to 9 . Which is 1 and 8 . Step 2 : (x + 1) (x + 5) Step 3: (x + 1) = 0 Transpose 1 to the right side x = -1 (x + 5) = 0 Transpose 5 to the right side x = -5 The final answer is : x = -1 and x = -5 Example no. 2: x ²  + 9x + 8= 0 Step 1 : To factorize the equation x ² + 9x + 8 = 0 , we need to break down the quadratic term ( 9x ) into two terms whose coefficients multiply to give 8 and add up to 9 . Which is 1 and 8 . Step 2 : Rewrite the equation (x + 1) (x +8) Step 3 : Find the value of x (x + 1) = 0 Transpose 1 to the right side x = -1 (x + 8. ).= 0 Transpose 8 to the right side x = -8 The final answer is : x = -1 and x = -8