How do you solve this?
1 answer:
You have correctly found a=2, b=5, c=3.
You know a > 0, so the parabola will open up.
If the parabola opens up, the vertex is a minimum.
Use the formula for the axis of symmetry.
.. x = -b/(2a) = -5/(2*2) = -5/4
.. f(-5/4) = 2(-5/4)^2 +5(-5/4) +3 = -1/8
The vertex is (-5/4, -1/8).
Use the formula for the discriminant.
.. b^2 -4ac = 5^2 -4*2*3 = 25 -24 = 1
This is positive and a perfect square, so there are 2 real roots. They are (1) rational and unequal.
Use the quadratic formula to tell you the roots.
.. x = -b/(2a) ±(√discriminant)/(2a)
.. = -5/4 ±√1/(2*2)
.. = -5/4 ±1/4
.. = {-3/2, -1}
You know a > 0, so the parabola will open up.
If the parabola opens up, the vertex is a minimum.
Use the formula for the axis of symmetry.
.. x = -b/(2a) = -5/(2*2) = -5/4
.. f(-5/4) = 2(-5/4)^2 +5(-5/4) +3 = -1/8
The vertex is (-5/4, -1/8).
Use the formula for the discriminant.
.. b^2 -4ac = 5^2 -4*2*3 = 25 -24 = 1
This is positive and a perfect square, so there are 2 real roots. They are (1) rational and unequal.
Use the quadratic formula to tell you the roots.
.. x = -b/(2a) ±(√discriminant)/(2a)
.. = -5/4 ±√1/(2*2)
.. = -5/4 ±1/4
.. = {-3/2, -1}
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In a right angle, the sum of the squares of the two shorter sides is equal to the square of the longest side.
Here, the longest side is 25, the shorter sides are x and x+5.
The length of a side must be a positive number, so x=15.
The answer is C.
Here, the longest side is 25, the shorter sides are x and x+5.
The length of a side must be a positive number, so x=15.
The answer is C.
