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
Answer:
3:1, 24 gallons blue 8 gallons yellow
Step-by-step explanation:
Jenny will use 24 gallons of blue paint and 8 gallons of yellow paint
Their ratio is 24:8 = 3:1
I believe that you are doing multiplication with this.
So… 9 x 3.65 = 32.85
Hope this helps. :)
A)1:2
b)21:2
c)6:44 or 3:22
d)2:5
The percentage of more juices that will be in the new package is 35.71%
<h3>What are word problems?</h3>
Word problems in mathematics are things happening in our daily life and we can use mathematical concepts and arithmetic operations to put a solution to those things.
From the given information, it was stated that:
- Almarai usually have 9 ounces of juice in each package, while
- Their new package will contain 14 ounces.
Our objective is to find the percentage of more juice that will be in the new package.
The percentage of more juice in the new package will be:
= 35.71%
Learn more about word problems here:
brainly.com/question/21405634
