Jonathan used completing the square to find the maximum value of the quadratic expression -x^2 - 4x + 1. What is the maximum val
ue of the expression, and at what x value does it occur?
1 answer:
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Answer:
10
Step-by-step explanation:
The radius is the magnitude of the complex number that is the difference between any point on the circle and the center point. A suitable calculator can tell you that magnitude:
║(8+7i) - (2-i)║ = √((8-2)² +(7-(-1))²) = √(36+64) = √100 = 10
Ignoring the triangle first off, it is just a parallelogram. We can find the area with:
(see first diagram).
Next, we need to find the area of the triangle. Its a right angle triangle, so the area can be found by:
where w and l are the lengths of the two smaller sides. We have one, and the longer side (hypotenuse) so we can use Pythagoras' Theorem to find the other small side (see second diagram).
Then find the area:
Take the area of the triangle away from the area of the paralellogram:
Next, we need to find the area of the triangle. Its a right angle triangle, so the area can be found by:
where w and l are the lengths of the two smaller sides. We have one, and the longer side (hypotenuse) so we can use Pythagoras' Theorem to find the other small side (see second diagram).
Then find the area:
Take the area of the triangle away from the area of the paralellogram: