Vertex form:
y-k=a(x-h)^2
h=-2,k=-20,y=-12 when x=0
thus;
-12+20=a(0+2)^2
8=4a
a=2
Equation:
y+20=2(x+2)^2
y+20=2(x^2+4x+4)
f(x)=2(x^2+4x+4)-20
f(x)=2x^2+8x+8-20
f(x)=2x^2+8x-20
Answer:
216.5
Step-by-step explanation:
866/4
216.5
If you learned about the 45-45-90 triangle (which is isosceles), then the faster way is to know that the hypotenuse (side opposite of right angle) is √2 times either one of the sides.
3√2 = (√2)x
x = 3
But if you didn't learn the 45-45-90 triangle yet, that's ok.
Recall the trigonometric ratios for right triangles: sine (sin), cosine (cos), tangent (tan).
If your angle is x, then
sin(x) = opposite side / hypotenuse
cos(x) = adjacent side / hypotenuse
tan(x) = opposite side / adjacent side
Remember the hypotenuse is the side opposite and across from the right angle (3√2 in this case).
An acronym to remember this is SohCahToa.
In this problem, the angle given is 45°, and you need to find the length of the adjacent side x. The hypotenuse is also given as 3√2.
Because we have the adjacent side and the hypotenuse, we use cosine to relate those two sides
cos(45°) = x / (3√2)
x = (3√2)cos45°
If you plug this into your calculator (in degree mode), then
x = 3
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