in short, you simply pick a few random "x" values, to get the "y", and that's your point, for example say x = 2, then y = -(2)² - 4 => y = -8, that gives us the point of (2, -8), and so on.
we can start off by finding the vertex, the U-turn of the graph, and then just pick a point to its left side and a point to its right side, and we can get the vertex of that by
![\bf y=-4x^2-4\implies y=-4x^2+0x-4 \\\\[-0.35em] ~\dotfill\\\\ \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-4}x^2\stackrel{\stackrel{b}{\downarrow }}{+0}x\stackrel{\stackrel{c}{\downarrow }}{-4} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{0}{2(-4)}~,~-4-\cfrac{0}{4(-4)} \right)\implies (0~,~-4-0)\implies (0,-4)](https://tex.z-dn.net/?f=%5Cbf%20y%3D-4x%5E2-4%5Cimplies%20y%3D-4x%5E2%2B0x-4%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ctextit%7Bvertex%20of%20a%20vertical%20parabola%2C%20using%20coefficients%7D%20%5C%5C%5C%5C%20y%3D%5Cstackrel%7B%5Cstackrel%7Ba%7D%7B%5Cdownarrow%20%7D%7D%7B-4%7Dx%5E2%5Cstackrel%7B%5Cstackrel%7Bb%7D%7B%5Cdownarrow%20%7D%7D%7B%2B0%7Dx%5Cstackrel%7B%5Cstackrel%7Bc%7D%7B%5Cdownarrow%20%7D%7D%7B-4%7D%20%5Cqquad%20%5Cqquad%20%5Cleft%28-%5Ccfrac%7B%20b%7D%7B2%20a%7D~~~~%20%2C~~~~%20c-%5Ccfrac%7B%20b%5E2%7D%7B4%20a%7D%5Cright%29%20%5C%5C%5C%5C%5C%5C%20%5Cleft%28-%5Ccfrac%7B0%7D%7B2%28-4%29%7D~%2C~-4-%5Ccfrac%7B0%7D%7B4%28-4%29%7D%20%5Cright%29%5Cimplies%20%280~%2C~-4-0%29%5Cimplies%20%280%2C-4%29)
and since it's a vertical parabola, the axis of symmetry comes from the x-coordinate of the vertex, namely x = 0, check the picture below.
Answer:
A. England = 56000000
B. 1.046 * 10^7
C. 9.7 to 2sf
Step-by-step explanation:
A. England = 5.60*10000000
=56000000
B. Wale = 3.14*1000000 = 3140000
Scotland = 5.44*1000000 = 5440000
Northern Ireland = 1.88*1000000 =1880000
Total = 10460000
In standard form =1.046*10^7
C. Total population as at 2018 = 66460000
expected population by 2041 = 72900000
increase or change = (72900000 - 66460000) = 6440000
% change = (6440000/66460000)*100
= 0.0969003912 * 100
= 9.69003912
= 9.7 to 2sf
Answer:
8 units is the answer.
Step-by-step explanation:
Pythagorean theorem can be written as,
∴ d = 8 units
Answer:
H0 : μ1 = μ2
H0 : μ1 < μ2
Step-by-step explanation:
Given :
Early studiers, group 1, mean μ1
Late studiers, group 2 ; mean, μ2
To test the claim that students who study earlier have an average score that is less than the average score for students
The null hypothesis ; there is no difference in average score
H0 : μ1 = μ2
Alternative hypothesis is early studiers means is less than average score of late studiers
H0 : μ1 < μ2
