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

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

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 = (-b \± √(b^2 - 4ac))/(2a)`

Where

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

`x = (-7 \± √(7^2 - 4*3*-3))/(2*3)`

`x = (-7 \± √(49+ 36))/(6)`

`x = (-7 \± √(85))/(6)`

`x = (-7 \± 9.22)/(6)`

Split

`x = (-7 + 9.22)/(6)\ or\ x = (-7 - 9.22)/(6)`

`x = (2.22)/(6)\ or\ x = (-16.22)/(6)`

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