The first steps in writing f(x) = 3x2 – 24x 10 in vertex form are shown. f(x) = 3(x2 – 8x) 10 (startfraction negative 8 over 2 e
2 answers:
The given quadratic equation 3x^2 – 24x + 10 can be written in vertex form that is f(x) = 3(x – 4)2 – 38.
<h3>What are quadratic equations?</h3>A quadratic equation is an equation of degree 2 and the standard form of a quadratic equation where x is the variable and a,b, c are real numbers.
Following the steps already shown to transform the given function into the vertex form,
Therefore, the function written in vertex form is f(x) = 3(x – 4)2 – 38.
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i) The given function is
The domain is
ii) For vertical asymptotes, we simplify the function to get;
The vertical asymptote occurs at
iii) The roots are the x-intercepts of the reduced fraction.
Equate the numerator of the reduced fraction to zero.
iv) To find the y-intercept, we substitute into the reduced fraction.
v) The horizontal asymptote is given by;
The horizontal asymptote is .
vi) The function has a hole at .
Thus at .
This is the factor common to both the numerator and the denominator.
vii) The function is a proper rational function.
Proper rational functions do not have oblique asymptotes.
