Answer:
(- 2, - 1 )
Step-by-step explanation:
Given the 2 equations
2x - 3y = - 1 → (1)
x + 4y = - 6 → (2)
Rearrange (2) expressing x in terms of y by subtracting 4y from both sides
x = - 6 - 4y → (3)
Substitute x = - 6 - 4y into (1)
2(- 6 - 4y) - 3y = - 1 ← distribute and simplify left side
- 12 - 8y - 3y = - 1
- 12 - 11y = - 1 ( add 12 to both sides )
- 11y = 11 ( divide both sides by - 11 )
y = - 1
Substitute y = - 1 into (3) for corresponding value of x
x = - 6 - 4(- 1) = - 6 + 4 = - 2
Solution is (- 2, - 1 )
The vertex form of a quadratic function is:
f(x) = a(x - h)² + k
The coordinate (h, k) represents a parabola's vertex.
In order to convert a quadratic function in standard form to the vertex form, we can complete the square.
y = 2x² - 5x + 13
Move the constant, 13, to the other side of the equation by subtracting it from both sides of the equation.
y - 13 = 2x² - 5x
Factor out 2 on the right side of the equation.
y - 13 = 2(x² - 2.5x)
Add (b/2)² to both sides of the equation, but remember that since we factored 2 out on the right side of the equation we have to multiply (b/2)² by 2 again on the left side.
y - 13 + 2(2.5/2)² = 2(x² - 2.5x + (2.5/2)²)
y - 13 + 3.125 = 2(x² - 2.5x + 1.5625)
Add the constants on the left and factor the expression on the right to a perfect square.
y - 9.875 = 2(x - 1.25)²
Now, we need y to be by itself again so add 9.875 back to both sides of the equation to move it back to the right side.
y = 2(x - 1.25)² + 9.875
Vertex: (1.25, 9.875)
Solution: y = 2(x - 1.25)² + 9.875
Or if you prefer fractions
y = 2(x - 5/4)² + 79/8
Make an inference about which fish increased its predicted average population from Year 1 to Year 2.
All three types of fish increased their predicted average population.
Trout increased its predicted average population.
Bass increased its predicted average population.
None of the fish increased their predicted average population.
