Answer: x = (-4 + √22) / 4 and also x = (-4 - √22) / 4
Explanation:
To find the x-intercepts of the quadratic function f(x) = 8x^2 + 16x - 3, we need to set f(x) equal to zero and solve for x.
Setting f(x) = 0, we have:
8x^2 + 16x - 3 = 0
To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 8, b = 16, and c = -3. Substituting these values into the quadratic formula, we get:
x = (-16 ± √(16^2 - 4(8)(-3))) / (2(8))
Simplifying further, we have:
x = (-16 ± √(256 + 96)) / 16
x = (-16 ± √352) / 16
Now, we can simplify the expression under the square root:
x = (-16 ± √(16 * 22)) / 16
x = (-16 ± 4√22) / 16
Finally, we can simplify the expression further by factoring out a common factor of 4:
x = (-4 ± √22) / 4
The x-intercepts of the function f(x) = 8x^2 + 16x - 3 are:
x = (-4 + √22) / 4
x = (-4 - √22) / 4
These are the two values of x where the function intersects the x-axis.