Question

Write an equation for the lowest-degree polynomial function, with the graph and intercepts shown in the figure. For this exercise, make the leading coefficient be 1 or -1

Answer 1

Answer:

f(x)  = (x+1)² - 9

Step-by-step explanation:

We can start by seeing if this is a quadratic function, as that is the lowest degree polynomial possible.

The vertex form for a quadratic function is a(x-h)² + k, with the vertex being (h, k).

In this example, the leading coefficient (a) must be 1 or -1. If a is positive, the graph opens upward, and vice versa. Since the graph opens upward, a must be 1.

Our vertex in this picture is (-1, -9). We can plug those values in, along with a=1, to get

1(x-(-1))² - 9 = (x+1)² - 9

Therefore, our equation is f(x)  = (x+1)² - 9

Answer 2

The polynomial is given by:

$p(x) = x^2 + 2x - 8$

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Zeros of a function:

Given a polynomial f(x), this polynomial has roots $x_{1}, x_{2}, x_{n}$ such that it can be written as: $a(x - x_{1})*(x - x_{2})*...*(x-x_n)$, in which a is the leading coefficient.

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• The polynomial has two x-intercepts, thus, the lowest-degree is 2.
• Concave up, thus, the leading coefficient is $a = 1$.
• The x-intercepts are $x_1 = -4, x_2 = 2$, and thus:

$p(x) = (x - (-4))(x - 2) = (x + 4)(x - 2) = x^2 + 4x - 2x - 8 = x^2 + 2x - 8$

A similar problem is given at https://brainly.com/question/22817243