Trigonomitry
Find the value of sin(30 degrees)
sin(30)=1/2
x + y = 9, y = 5
x = 4
Evaluate x^2 - 3x when x = 4.
16 - 12 = 4
State the vertex of y = ( x − 1 ) 2 + 4
( 1, 4 )
Factor x^2 + 6x
x(x + 6)
In a right triangle, the opposite side is 6 cm and the hypotenuse is 10 cm. Find sin(0)
sin(θ)= 6/10= 3/5
y = x + 3, 2x + y = 11
2x + (x + 3) = 11 -> 3x = 8 -> x = 8/3 , y = 17/3
Does y = −x^2 + 6x − 1 open up or down?
Opens down (negative coefficient)
Does y = −3 ( x + 2 ) 2 + 1 open up or down?
Opens down
Factor x^2 − 16
( x − 4 ) ( x + 4 )
In a right triangle, the adjacent side is 8 cm and the hypotenuse is 17 cm. Find cos(0).
cos(0)= 8/17
x + y = 7, x − y = 1
2x = 8 -> x = 4, y = 3
Identify the y-intercept of y = x^2 − 5x + 6
y = 6
Rewrite y = x2 + 4x + 1 in vertex form.
y= ( x + 2 )^2 - 3
Factor x^2 + 5x + 6
( x + 2 ) ( x + 3 )
Find 0, to the nearest degree, if sin(0)= 0.45
0 = sin − 1(0.45) = around 27 degrees
Determine the number of solutions
y = 2x − 1 , 2y = 4x − 2
Both equations simplify to the same line -> infinite solutions
Find the axis of symmetry of y= x^2 − 8x + 3y
x = 2/8 = 4
Find the minimum value of y =2( x − 3 )^2 − 5
-5
Solve x^2 − 7x =0.
x = 0, 7
A tree casts a shadow 12 m long. The angle of elevation of the sun is 38 degrees. Find the height of the tree.
tan (38 degrees)= 12h -> h = 12tan(38∘) = around 9.4 m
Two numbers add to 28. One is 4 more than the other. Find the numbers.
x + y = 28, x = y + 4
2y = 24 -> y = 12, x = 16
The height of a ball is h(t)=−2t^2 + 8t + 1. When is the height maximum?
t = -8/2(−2) = 2 seconds
A parabola has vertex (2, –1) and passes through (0, 7). Find its equation.
y= 2( x − 2)^2 - 1
The area of a rectangle is x^2 − x − 12. Find the dimensions.
(x − 4) (x + 3)