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.

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 $a \ne 0$.

Answer: $\boxed{f(x) = ax^2 + bx + c}$

A quadratic equation is a polynomial equation of the second degree. Its general form is $ax^2 + bx + c = 0$, where $a \ne 0$.

Answer: $\boxed{ax^2 + bx + c = 0}$

The graph of a quadratic function is always in the shape of a parabola.

Answer: parabola

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:

$$\sqrt{x^2} = \pm\sqrt{16}$$ $$x = \pm 4$$

Answer: $\boxed{x = \pm 4}$

The statement "If $(a)(b) = 0$ then $a = 0$ or $b = 0$" describes the Zero Product Property.

Answer: Zero Product Property

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 $(1, 7)$:

$$7 = a(1)^2 + b(1) + 4$$ $$7 = a + b + 4$$ $$a + b = 3 \quad \text{(Equation 1)}$$

Using the point $(2, 16)$:

$$16 = a(2)^2 + b(2) + 4$$ $$16 = 4a + 2b + 4$$ $$12 = 4a + 2b$$

Divide by 2:

$$6 = 2a + b \quad \text{(Equation 2)}$$

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: $\boxed{y = 3x^2 + 4}$