Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -2x2 + 2x + 6
answers available, which one is correct?
{–1.30, 2.30}
{-2, 2}
{–1.00, –3.00}
{–0.33, 0.33}
f(x) = -2(x^2-x) + 6
= -2(x^2 - x + 1/4) + 6 + 2(1/4)
= -2(x - 1/2)^2 + 13/2
f(x)=0 when
(x - 1/2)^2 = 13/4
x = (1±√13)/2
. . .
To find the approximate values of x that are solutions to f(x) = 0, we can use the quadratic formula.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
For the given quadratic function f(x) = -2x^2 + 2x + 6, we have:
a = -2, b = 2, and c = 6.
Plugging these values into the quadratic formula:
x = (-2 ± √(2^2 - 4(-2)(6))) / (2(-2))
x = (-2 ± √(4 + 48)) / (-4)
x = (-2 ± √52) / -4
x = (-2 ± 2√13) / -4
x = (1 ± √13) / 2
So, the approximate values of x that are solutions to f(x) = 0 are {–1.30, 2.30}.
Therefore, the correct answer is: {–1.30, 2.30}.
To find the approximate values of x that are solutions to the equation f(x) = 0, where f(x) = -2x^2 + 2x + 6, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = -2, b = 2, and c = 6. Substituting these values into the quadratic formula, we get:
x = (-2 ± √(2^2 - 4(-2)(6))) / (2(-2))
= (-2 ± √(4 + 48)) / (-4)
= (-2 ± √52) / (-4)
= (-2 ± 2√13) / (-4)
Simplifying further:
x = (-1 ± √13) / 2
Now we need to find the approximate values of x. From the given answer choices, we can see that only {-1.30, 2.30} match the form (-1 ± √13) / 2. Thus, the correct answer is:
{–1.30, 2.30}