We're back with some more algebra fun! 🎈Let's look at this quadratic equation: f(x) = -x² - 2x + 9.
We're aiming to find when f(x) = 0, so the equation becomes -x² - 2x + 9 = 0.
As per the quadratic formula, the solutions for x in a quadratic equation of the form ax² + bx + c = 0 are given by x = [-b ± sqrt(b² - 4ac)] / (2a).
For our given equation, a = -1, b = -2, and c = 9.
Let's substitute these into the quadratic formula and see what we get:
x = [2 ± sqrt((-2)² - 4*(-1)9)] / (2(-1))
x = [2 ± sqrt(4 + 36)] / -2
x = [2 ± sqrt(40)] / -2
When you simplify that, we get:
x = [2 ± 2sqrt(10)] / -2
This can be further simplified to:
x = -1 ± sqrt(10)
If we work this out on a calculator, we get:
x ≈ -1 - 3.16 and -1 + 3.16
x ≈ -4.16 and 2.16
So, the answer that matches our calculated solutions is option C) x ≈ 2.16 and -4.16!
Hope that makes sense, and remember, math is just like lifting weights for your brain, the more you do, the stronger it gets! 💪🧠
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