Question

Fred's teacher gave the class the quadratic function f(x) = 4x² + 16x+9.

State two different methods Fred could use to solve the equation f(x) = 0. Using one of the methods stated in part a, solve f(x) = 0 for x, to the nearest
tenth.

Answer 1

There are two methods to solve the quadratic equation f(x) = 4x² + 16x + 9 = 0: factoring and quadratic formula. Using the quadratic formula, the solutions for x are approximately -2.1 and -1.9.

Step-by-step explanation:

To solve the quadratic equation f(x) = 4x² + 16x + 9 = 0, Fred can use two different methods: factoring and quadratic formula.

Method 1: Factoring:

Step 1: Rewrite the quadratic equation in the form ax² + bx + c = 0.

Step 2: Factor the quadratic equation.

Step 3: Set each factor equal to 0 and solve for x.

Method 2: Quadratic Formula:

Step 1: Identify the values of a, b, and c in the quadratic equation.

Step 2: Substitute the values into the quadratic formula: x = (-b ± √(b² - 4ac))/(2a).

Step 3: Simplify the equation using the formula and solve for x.

To solve f(x) = 0 using the Quadratic Formula, we have a = 4, b = 16, and c = 9. Substituting these values into the quadratic formula, we get x = (-16 ± √(16² - 4(4)(9)))/(2(4)). Solving this equation, we find two solutions for x, approximately -2.1 and -1.9.