(x-h)^2=4P(y-k), vertex is (h,k)
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k
nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix
I will only convert the 1st one fully, you should be able to do the rest
1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)
k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5
basically completee the square with x and find P by force factoring a 4 out
2. directix: y=-1.75
3. directix: y=1.5
4. directix: y=17.25
5. d: -37.5
6. d: 9.25
7. d=2.625
order them yourself
Answer:
inequality form: x 
-2 or x > 3
interval notation form: (-∞,-2] ∪ (3,∞)
Step-by-step explanation:
I attached a picture that shows all the work. You begin by isolating then solving for x on both sides. Then form a solution using the information found out about x. For example, you can combine the found inequalities for x to solve that x must be GREATER than 3 while being LESS than -2. Using that you can form an line and make a line. Remember, when writing in interval notation form you always begin from the left to the right (in reference) to the number line.
How do linear, quadratic, and exponential functions compare?
Answer:
How can all the solutions to an equation in two variables be represented?
<u><em>The solution to a system of linear equations in two variables is any ordered pair x,y which satisfies each equation independently. U can Graph, solutions are points at which the lines intersect.</em></u>
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<u><em>How can all the solutions to an equation in two variables be represented?</em></u>
<u><em>you can solve it by Iterative method and Newton Raphson's method.</em></u>
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<u><em>How are solutions to a system of nonlinear equations found?
</em></u>
Solve the linear equation for one variable.
Substitute the value of the variable into the nonlinear equation.
Solve the nonlinear equation for the variable.
Substitute the solution(s) into either equation to solve for the other variable.
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</em></u>
<u><em>How can solutions to a system of nonlinear equations be approximated? U can find the solutions to a system of nonlinear equations by finding the points of intersection. The points of intersection give us an x value and a y value. Using the example system of nonlinear equations, let's look at how u can find approximate solutions.</em></u>
The slope is 1 because it is parallel and y=x+b, so, 2=-3+b and b=5
y=x+5
Answer:
X = 12
Y = 4
Step-by-step explanation:
X + Y = 16
X = 3Y
3Y + Y = 16
4Y = 16
Y = 4
X + 4 = 16
X = 12
