Which quadratic equation has a vertex at (4, 2)?
1 answer:
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9514 1404 393
Answer:
- circle
- y-axis
- 5 units
Step-by-step explanation:
It can be helpful to actually see the graph. For 0 ≤ θ ≤ π, a circle is developed above the x-axis, symmetrical about the y-axis (θ=π/2). For π ≤ θ ≤ 2π, the same circle is traced again in the same direction (CCW), as values of r are negative for those angles.
The circle has a radius of 2.5, centered at (0, 2.5), so the diameter is 5 units. The length of the diameter is the farthest distance between any two points on a circle.
So since its a right triangle, we can use the pythagorean theorem, which is . Since we know that 2 and 3 are our legs and x is our hypotenuse, we can solve the equation as such:
Since √13 can't be further simplified, that is your final answer.