Question

write a quadratic equation for the points (2,0) and (12,5). make sure to include the axis and five points used to graph the parabola

Answer 1

Using the Factor Theorem, the parabola is given by: $f(x) = 0.05(x^2 - 4x + 4)$

The graph is sketched at the end of this answer.

The Factor Theorem states that a polynomial function with roots is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

In this problem:

• The graph is a parabola, which means that the function is of the 2nd degree.
• One zero, with multiplicity 2, at $x = 2$, hence, $x_1 = x_2 = 2$.

Then:

$f(x) = a(x - 2)(x - 2)$

$f(x) = a(x^2 - 4x + 4)$

Point (12,5) means that when $x = 12, y = 5$, and this is used to find a.

$f(x) = a(x^2 - 4x + 4)$

$5 = a(12^2 - 4(12) + 4)$

$100a = 5$

$a = \frac{5}{100}$

$a = 0.05$

Hence, the parabola is:

$f(x) = 0.05(x^2 - 4x + 4)$

At the end of this answer, the graph with five points is sketched.

A similar problem is given at https://brainly.com/question/24380382