Quadratic Equations and Their Solutions

The video tutorial covers solving quadratic equations using different methods. It begins with factoring a trinomial where the leading coefficient is one, finding the roots, and identifying the correct solution. The next section focuses on finding the sum of solutions for a quadratic equation by factoring and adding fractions with different denominators. The final section demonstrates using the quadratic formula to solve equations, including calculating the discriminant and simplifying the expression to find the roots.

What is the first step in solving the equation f(x) = x^2 + 8x + 3 when f(x) = 51?

• Replace f(x) with 51

• Divide both sides by 51

• Add 51 to both sides

• Multiply both sides by 51

Which pair of numbers is used to factor the trinomial x^2 + 8x - 48?

• -8 and 6

• 8 and -6

• -4 and 12

• 4 and 12

What is the value of x when solving the equation x^2 + 8x - 48 = 0?

• x = -4

• x = 4

• x = 12

• x = -12

What is the first step in finding the sum of solutions for the equation 6k^2 + k - 12 = 0?

• Divide the leading coefficient by the constant term

• Subtract the leading coefficient from the constant term

• Add the leading coefficient to the constant term

• Multiply the leading coefficient by the constant term

Which two numbers multiply to -72 and add to 1 in the equation 6k^2 + k - 12 = 0?

• 8 and 9

• -8 and 9

• -6 and 12

• 6 and -12

What is the sum of the solutions for the equation 6k^2 + k - 12 = 0?

• -1/3

• 1/6

• 1/3

• -1/6

What is the quadratic formula used to solve equations of the form ax^2 + bx + c?

• x = b ± √(b^2 - 4ac) / a

• x = -b ± √(b^2 - 4ac) / 2a

• x = b ± √(b^2 + 4ac) / 2a

• x = -b ± √(b^2 + 4ac) / a

In the quadratic formula, what is the value of b for the equation 4y^2 - 2y - 7 = 0?

• -7

• 2

• -2

• 4

What is the simplified form of the solution for the equation 4y^2 - 2y - 7 = 0 using the quadratic formula?

• 1 ± √29 / 4

• -1 ± √29 / 2

• -1 ± √29 / 4

• 1 ± √29 / 2

What is the first step in simplifying the expression under the square root in the quadratic formula for 4y^2 - 2y - 7 = 0?

• Calculate b^2

• Calculate 4ac

• Add b^2 and 4ac

• Subtract 4ac from b^2