What are the definitions of a quadratic function, quadratic equation, and parabola? Solve x2 = 16 and identify the Zero Product Property. Find the quadratic equation from a table of values.

Step 1: Answer Question 1. A polynomial function of the second degree is also known as a quadratic function. Its general form is f(x) = ax^2 + bx + c, where a 0. Answer: f(x) = ax^2 + bx + c Step 2: Answer Question 2. A quadratic equation is a polynomial equation of the second degree. Its general form is ax^2 + bx + c = 0, where a 0. Answer: ax^2 + bx + c = 0 Step 3: Answer Question 3. The graph of a quadratic function is always in the shape of a parabola. Answer: parabola Step 4: Answer Question 4 by solving the quadratic equation. Given the equation: x^2 = 16 To solve for x, take the square root of both sides, remembering to include both positive and negative roots: sqrt(x^2) = ±sqrt(16) x = ± 4 Answer: x = ± 4 Step 5: Answer Question 5. The statement "If (a)(b) = 0 then a = 0 or b = 0" describes the Zero Product Property. Answer: Zero Product Property Step 6: Answer Question 6 by finding the quadratic equation from the table of values. A quadratic equation has the form y = ax^2 + bx + c. Using the point (0, 4): 4 = a(0)^2 + b(0) + c 4 = c So, the equation becomes y = ax^2 + bx + 4. Using the point (1, 7): 7 = a(1)^2 + b(1) + 4 7 = a + b + 4 a + b = 3 (Equation 1) Using the point (2, 16): 16 = a(2)^2 + b(2) + 4 16 = 4a + 2b + 4 12 = 4a + 2b Divide by 2: 6 = 2a + b (Equation 2) Now, solve the system of equations for a and b: Subtract Equation 1 from Equation 2: (2a + b) - (a + b) = 6 - 3 a = 3 Substitute a=3 into Equation 1: 3 + b = 3 b = 0 So, a=3, b=0, and c=4. The quadratic equation is y = 3x^2 + 0x + 4, which simplifies to y = 3x^2 + 4. Answer: y = 3x^2 + 4 Last free one today — make it count tomorrow, or type /upgrade for unlimited.