An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression a x squared
1 answer:
The polynomial is prime because the provided polynomial can not be factored shown in the X-method chart.
<h3>What is X method?</h3>X-method is the method to find the factors of the polynomial equation.
An x-method chart shows the product a c at the top of x and b at the bottom of x.
Above the chart is the expression,
The given polynomial in the problem is,
Let's check if the factors of polynomial. To find the factor, we need, to find the two number whose sum or different is 8 and the product is 6 (6 × 1).
As there is no number which gives has the sum or different is 8 and the product is 6 (6 × 1). Thus, the above polynomial can not be factored. Thus this polynomial is prime.
Thus, the polynomial is prime because the provided polynomial can not be factored, shown in the X-method chart.
Learn more about the X method here;
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Solution:
Given:
Part A:
The vertex of an up-down facing parabola of the form;
Rewriting the equation given;
Therefore, the vertex is (0,0)
Part B:
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)
Using the standard equation of a parabola;
Rewriting the equation in standard form,
Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)
Hence,
Therefore, the focus is;
Part C:
A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)
Using the standard equation of a parabola;
Rewriting the equation in standard form,
Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).
Hence,
Therefore, the directrix is;