Answer:
B
Step-by-step explanation:
Answer:
Step-by-step explanation:
The equation of a circle:
<em>(h, k)</em><em> - center</em>
<em>r</em><em> - radius</em>
<em />
We have diameter endpoints.
Half the length of the diameter is the length of the radius.
The center of the diameter is the center of the circle.
The formula of a distance between two points:
Substitute the coordinates of the given points (-8, 2) and (-2, 6):
The radius:
The formula of a midpoint:
Substitute:
Finally:
Answer:
2nd option will be the answer (y=4x²+48x+146)
Step-by-step explanation:
y=4(x+6)²+2
y=4(x²+2*x*6+6²)+2 [(a+b)²=a²+2ab+b²]
y=4(x²+12x+36)+2
y=4(x²)+4(12x)+4(36)+2
y=4x²+48x+144+2
y=4x²+48x+146
The attached picture is a summary of all the six transformations you'd do.
Any change outside the f(x) notation impacts y-values of points on the graph.
Any changes inside the f(x) notation impacts x-values of points on the graph.
The trick is that the inside changes are usually the opposite of what you'd expect to have happen.
7. y=f(x)+8
This is an outside change. You're adding 8 to all the y-values of points on the graph. This will shift your entire graph up 8 units.
8. y=f(x+6)
This is an inside change. Because it says "+6", you want to think, "Ah! That means I'll actually subtract 6 from the x-value of every point on the graph." This graph is shifted 6 units to the left.
9. y=-f(x)
Inside change, impacts y-values. Every y-value will be given the opposite signs. Negatives become positive and positives become negative. This will flip your graph over the x-axis.
10. y = f(-x) + 5
Give this one a shot on your own first in a comment and I'll let you know how you did.
11. y = - 3 f(x-3)
There are three things happening. A negative on the outside, multiplying by 3 on the outside, and subtracting 3 inside. What will each of those do individually? Take a shot on this one and let me know what you think.
12. y = 1/2 f( 1/2 x )
Again, three changes. Try this one and let me know what you think. Remember multiplying by 1/2 inside really means you'll do the opposite of multiplying by 1/2.
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
1 + tan²A = sec²A , secA = , cosecA = , cotA = , tanA =
Consider the left side
=
=
=
= × sin²A
=
= tanA = right side , thus proven