Question

In the coordinate plane, the equation of a vertical cross section of a certain satellite dish is shown below, where x and y coordinates are in meters. y = 1/30x²+2x+32 Type an equivalent expression for y in the form a(x + b)² + c. Type your response in the box below. 1​

Answer 1

To convert the given equation to the form a(x + b)² + c, we can complete the square. By following the steps, we obtain the equivalent expression y = (1/30)(x + 30)² + 2.

Step-by-step explanation:

The given equation is y = (1/30)x² + 2x + 32. We need to write an equivalent expression in the form a(x + b)² + c. To do this, we will complete the square.

Step 1: Rewrite the equation as y = (1/30)(x² + 60x) + 32.

Step 2: Add and subtract the square of half the coefficient of x, which is (60/2)² = 900. This gives us y = (1/30)(x² + 60x + 900 - 900) + 32.

Step 3: Factor the quadratic expression inside the parentheses. We have y = (1/30)((x + 30)² - 900) + 32.

Step 4: Simplify the expression by distributing the (1/30) and combining like terms. The final expression is y = (1/30)(x + 30)² - 30 + 32.

Step 5: Further simplify to obtain the equivalent expression in the form a(x + b)² + c. This gives us y = (1/30)(x + 30)² + 2.