The vertex of the given quadratic polynomial function is (6, 8)
A quadratic polynomial function is the one which can be represented in the form ax² + bx + c = y where a, b and c are coefficients and x, and y are independent and dependent variables respectively. A parabola is formed when the quadratic polynomial is plotted on graph. The x coordinate of the vertex can be found using formula (-b/2a) and y coordinate can be found by putting the value of x in the equation.
Given polynomial function x² - 12x + 44
Now, x = (-b/2a)
x = (12/2)
=> x = 6
Now, y = 6² - 12×6 + 44
y = 36 - 72 + 44
=> y = 8
Therefore, Vertex = (6, 8)
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Whole numbers<span><span>\greenD{\text{Whole numbers}}Whole numbers</span>start color greenD, W, h, o, l, e, space, n, u, m, b, e, r, s, end color greenD</span> are numbers that do not need to be represented with a fraction or decimal. Also, whole numbers cannot be negative. In other words, whole numbers are the counting numbers and zero.Examples of whole numbers:<span><span>4, 952, 0, 73<span>4,952,0,73</span></span>4, comma, 952, comma, 0, comma, 73</span>Integers<span><span>\blueD{\text{Integers}}Integers</span>start color blueD, I, n, t, e, g, e, r, s, end color blueD</span> are whole numbers and their opposites. Therefore, integers can be negative.Examples of integers:<span><span>12, 0, -9, -810<span>12,0,−9,−810</span></span>12, comma, 0, comma, minus, 9, comma, minus, 810</span>Rational numbers<span><span>\purpleD{\text{Rational numbers}}Rational numbers</span>start color purpleD, R, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color purpleD</span> are numbers that can be expressed as a fraction of two integers.Examples of rational numbers:<span><span>44, 0.\overline{12}, -\dfrac{18}5,\sqrt{36}<span>44,0.<span><span> <span>12</span></span> <span> </span></span>,−<span><span> 5</span> <span> <span>18</span></span><span> </span></span>,<span>√<span><span> <span>36</span></span> <span> </span></span></span></span></span>44, comma, 0, point, start overline, 12, end overline, comma, minus, start fraction, 18, divided by, 5, end fraction, comma, square root of, 36, end square root</span>Irrational numbers<span><span>\maroonD{\text{Irrational numbers}}Irrational numbers</span>start color maroonD, I, r, r, a, t, i, o, n, a, l, space, n, u, m, b, e, r, s, end color maroonD</span> are numbers that cannot be expressed as a fraction of two integers.Examples of irrational numbers:<span><span>-4\pi, \sqrt{3}<span>−4π,<span>√<span><span> 3</span> <span> </span></span></span></span></span>minus, 4, pi, comma, square root of, 3, end square root</span>How are the types of number related?The following diagram shows that all whole numbers are integers, and all integers are rational numbers. Numbers that are not rational are called irrational.
