Question

Question 12 (4 points) Describe the graph of f(x) = A - 7x2 - 6x under the following headings (show all calculations to support your answers): a) x- and y-intercept(s) b) end behaviours A/

Answer 1

Giren function is f(x) = a* _ 7x² - 6 Ex 24- = 0 a) To find x-intercept, we assume that f(m2 7x² - 64 5 x 3-754-6) Since (-1)² - 7 (-1)-6 +7-6 +6-6 o - is a root of polynomial x²_70-6 is a factor of +370 -6. Then by Synthetic division method for gla) = x3 + 0-78-6 at = > ñ 2+1 25-1, -6 다. 6 -1 -6 Remainder → 13 · 73-6 (x+1) (x²x-6) (x + 1) (re? s-6) = 0 c] = > 2 (2+) [X08-32 +2(4-3) ] = = x(2+i) {(x-3) (x+2)) = x(x+1) [ve 3x +27-6 204+1)(4-3)(x+2) = 3-0 ct x +1 so or or 24+2=0 3= 2 C-1 x=3 2-2 Thus the grintencepts of the given polynomial 1/2

given by 7m), are 1(0,0),(-2,0), (1,0) & (3,0) put. Now, to find yrintercepts of fem 720 f(0) = 0 - 7602) - 610) f(o)=0 y-intercept is (0,0) n Thus, b) Since f(x) has the leading term x4 and the 1 70 leading coefficient the power of variable 4 (eren) with xe is → "we get fra) and 0, we get f(a) the end Hence, be haviour of f(n) is given by food to -> and from x + त्र 2/2