Question

if the leading coefficient in the equation of the polynomial is 1, fill in the terms missing in the boxes. the equation of this polynomial is y = □ - 3x² - 4x + □. what is the degree of this polynomial? how do you know? explain. if a student says the maximum point of the graph is where there is a circle, is the student correct? explain.

Explanation:

Step1: Identify degree of polynomial

The highest - power of \(x\) in the polynomial \(y=- 3x^{2}-4x+\underline{}\) is 2. So the degree of the polynomial is 2.

Step2: Analyze maximum - point claim

A polynomial of degree 2 is a quadratic function of the form \(y = ax^{2}+bx + c\), and its graph is a parabola. A parabola has either a maximum or a minimum point. For \(y=-3x^{2}-4x + c\) (where \(a=-3<0\)), the parabola opens downwards and has a maximum point.

Answer:

The degree of the polynomial is 2. The student is correct because a quadratic polynomial (\(a
eq0\)) has a graph that is a parabola, and for \(a=-3<0\) in \(y = - 3x^{2}-4x + c\), the parabola opens downwards and has a maximum point.