how do i find parabola from a figure ( process )​

Step-by-step explanation:

The graph of a quadratic equation in two variables (y = ax^2 + bx + c ) is called a parabola. The following graphs are two typical parabolas their x-intercepts are marked by red dots, their y-intercepts are marked by a pink dot, and the vertex of each parabola is marked by a green dot: (Given in attachment for diagram)

We say that the first parabola opens upwards (is a U shape) and the second parabola opens downwards (is an upside down U shape). In order to graph a parabola we need to find its intercepts, vertex, and which way it opens.

Given y = ax^2 + bx + c , we have to go through the following steps to find the points and shape of any parabola:

Label a, b, and c.

Decide the direction of the paraola:

If a > 0 (positive) then the parabola opens upward.

If a < 0 (negative) then the parabola opens downward.

Find the x-intercepts:

Notice that the x-intercepts of any graph are points on the x-axis and therefore have y-coordinate 0. We can find these points by plugging 0 in for y and solving the resulting quadratic equation (0 = ax^2 + bx + c). If the equation factors we can find the points easily, but we may have to use the quadratic formula in some cases. If the solutions are imaginary, that means that the parabola has no x-intercepts (is strictly above or below the x-axis and never crosses it). If the solutions are real, but irrational (radicals) then we need to approximate their values and plot them.

Find the y-intercept:

The y-intercept of any graph is a point on the y-axis and therefore has x-coordinate 0. We can use this fact to find the y-intercepts by simply plugging 0 for x in the original equation and simplifying. Notice that if we plug in 0 for x we get: y = a(0)2 + b(0) + c or y = c. So the y-intercept of any parabola is always at (0,c).

Find the vertex (h,k):

To find the x-coordinate for the vertex we use the following formula:

To find the y-coordinate for the vertex we plug in h in the original equation:

k = a(h)2 + b(h) + c

Plot the points and graph the parabola  

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Minutes No. of Homework
Problems
2 or Less
3-4
5-6
7-8
9 or more 8
4
2
0
3

What is the number of homework problems that took less than 5 minutes in the given table?
A.
4
B.
14
C.
12
D.
8

Consider the sequence of steps to solve the equation: 3(x - 4) + 5x 9x - 36
Given => 3(x-4)+ 5x 9x - 36
Step 1 = 3x - 12 + 5x-9x - 36
Step 2 -> 3x + 5x - 12-9x - 36
Step 3 8x - 12 - 9x - 36
Step 48x - 8x - 12 - 9x - 8x - 36
Step 5 => 0 - 12 - x - 36
Step 6-12 - 36
Step 7-12 + 36 x - 36 + 36
Step 8 = 24 x +0
Step 9 = 24 - x
Which property yields Step 1?
3)
A)
Distributive Property
B)
Multiplicative Identity
Multiplication Property of Equality

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Round to the nearest tenth.

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If it regularly sells for $270, what is the
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15 cm
X
35°
909

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Jonah wants to make a one-sample
z
zz interval using
99
%
99%99, percent confidence to estimate what proportion of silicon wafers at his factory are defective. He wants the margin of error to be no more than
3
%
3%3, percent. A previous study suggests that about
6
%
6%6, percent of these wafers are defective.
If we assume
p
^
=
0.06
p
^
​
=0.06p, with, hat, on top, equals, 0, point, 06, what is the smallest sample size required to obtain the desired margin of error?

Add and check 5,655+7,978

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Yes or no and explain

Define Hypotenus
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you have the following coins in your pocket five quarters six dimes two nickels and 12 pennies what is the probability as a decimal you would draw a dime.
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Determine the equation of the quadratic function shown below.

find the midpoint of (-1,2) (-4,-9)

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