Question

Two quadratic functions are given. ()=−2−2+6 ()=22+5+3 Identify all values of x, to the nearest tenth, for which f (x) = g(x). A. –2.7 B. –1.8 C. –0.6 D. 0.4 E. 4.1 F. 5.1 G. 7.0

Answer 1

Answer:

$(a)\ x = 0.4\ or\ (d)\ x = -2.7$

Step-by-step explanation:

Given

$f(x) = -x^2 - 2x +6$

$g(x) = 2x^2 + 5x + 3$

Required

Find x if $f(x) = g(x)$

The above implies that:

$-x^2 -2x +6 = 2x^2 + 5x +3$

Collect like terms

$2x^2 + x^2 + 5x + 2x + 3 - 6 = 0$

$3x^2 + 7x - 3 = 0$

Using quadratic formula, we have;

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

Where

$a=3; b=7; c=-3$

$x = \frac{-7 \± \sqrt{7^2 - 4*3*-3}}{2*3}$

$x = \frac{-7 \± \sqrt{49+ 36}}{6}$

$x = \frac{-7 \± \sqrt{85}}{6}$

$x = \frac{-7 \± 9.22}{6}$

Split

$x = \frac{-7 + 9.22}{6}\ or\ x = \frac{-7 - 9.22}{6}$

$x = \frac{2.22}{6}\ or\ x = \frac{-16.22}{6}$

$x = 0.4\ or\ x = -2.7$ --- approximated