Vertex form is y=a(x-h)^2+k, so we can rearrange to that form...
y=3x^2-6x+2 subtract 2 from both sides
y-2=3x^2-6x divide both sides by 3
(y-2)/3=x^2-2x, halve the linear coefficient, square it, add it to both sides...in this case: (-2/2)^2=1 so
(y-2)/3+1=x^2-2x+1 now the right side is a perfect square
(y-2+3)/3=(x-1)^2
(y+1)/3=(x-1)^2 multiply both sides by 3
y+1=3(x-1)^2 subtract 1 from both sides
y=3(x-1)^2-1 so the vertex is:
(1, -1)
...
Now if you'd like you can commit to memory the vertex point for any parabola so you don't have to do the calculations like what we did above. The vertex of any quadratic (parabola), ax^2+bx+c is:
x= -b/(2a), y= (4ac-b^2)/(4a)
Then you will always be able to do a quick calculation of the vertex :)
X= 19/12 which is 1.58 in decimal form
Answer:
15.
Step-by-step explanation:
8x - 10 = 110 (vertical angles are equal in measure).
8x - 10+ 10 = 110 + 10
8x = 120
x = 120 /8
x = 15.
Answer:
Length: 40 Width: 76
Step-by-step explanation:
W is width, and L is length.
We know that the length is 36 less than the width, so L = w - 36. Two times the width plus two times the length equals the perimeter, so set up the equation for the perimeter as:
232 = 2w + 2(w-36)
Now solve for w:
232 = 2w + 2w - 72
304 = 4w
w = 76
we now know that the width is 76, so solve for the length:
L= 76-36
L = 40
Side a = 10.98991
Side b = 11.69522
Side c = 4
Angle ∠A = 70° = 1.22173 rad = 7/18π
Angle ∠B = 90° = 1.5708 rad = π/2
Angle ∠C = 20° = 0.34907 rad = π/9
