"SLC-S22W4//Linear and Quadratic equations equations."

Source

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Explain the difference between linear and quadratic equations. Provide examples of each type of system of equation and describe their general forms.

Differences

General Form

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In terms of graph plotting, linear equation forms a straight line, with one solution if there is no contradiction whereas quadratic equation forms a parabola with two solutions.

Examples:

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• Describe methods for solving quadratic equations and share the pros and cons for each method.

The Method For Solving Quadratic Equations

• Factoring
  Let's express the quadratic equation in factored form as ax^2 + bx + c = (px + q)(rx + s) = 0 and solve for x by setting each of the factors to 0.

Example: x^2 - 5x + 6 = 0
The factor is (x - 2)(x - 3) = 0, so (x = 2) or (x = 3)

The good part of the method is that it doesn't need advanced techniques, and it is very quick and simple for any equation that can be easily factored. However, the bad part of it is that it is not practical and has non or complex factorable equations and also it only works when the quadratic can be factored.

• Completing the Square
  This means rewriting the square in the form of (x - h)^2 = k) and then solve for x

Example: x^2 - 4x + 3 = 0
We can rewrite it as (x - 2)^2 = 1, so then x = 2 ±1 giving x = 3 or x = 1

• Quadratic Formula:
  Here we can give given formula below to find the solution.

Example

The above is an example of a quadratic equation method.

• Graphing:
  In a graph we can plot the quadratic equationy = ax^2 + bx + c as seen in the graph shared below to help us identify where the curve and the z-axis roots intersect.

Example: x = 2 and x = 3 are the intercepts.

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Solve for linear equation 3x + 2 = 11 and show value of x?

Solve for this quadratic equation x^2 + 2x - 6 = 0.

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Scenario number 1:

Suppose Ali has $15 to spend on snacks. He is buying a pack of chips for $3. How much money he have left? Suppose x is the amount of money Ali has left. Equation: x + 3 = 15 Share a solution for x
(Solve the above scenario-based questions and share step-by-step how you reach your outcome)

Based on the given scenario: **Ali has $15 for spending on snacks, and he spends $3 on a pack of chips. For us to find out how much money Ali has left, we will let x represent the amount of money left.

Given Equation: x + 3 = 15

Step-by-step solution

• Begin with the given equation

x + 3 = 15

• Substitute 3 from both sides to isolate x

x + 3 - 3 = 15 - 3

• Simplify both sides

x = 12

outcome:
Ali has $12 left with him, after buying the pack of chips.

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Scenario number 2:

Suppose there's a ball that is thrown in an upward direction from the ground with an initial velocity of 20 m/s and the height of the ball above ground is presented by the following equation; h(t) = -5t^2 + 20t Here h is height in meters and t is time in seconds. Share about the maximum height reached by this ball! Please solve for h!

For us to find the maximum height reached by the ball we will need to determine the time t at which the ball reaches its maximum height. This happens at the vertex of the parabola represented by the equation:

h(t) = -5t^2 + 20t

Step-by-step solution
If we are to present it in the form of quadratic equation h(t) = at^2 + bt + c, the time t at the vertex is given by:

t = - b/2a
Here, a = - 5 and b = 20

• Solve for t
  center>t = - 20/2(-5 )= 20/10 = 20 seconds

• Calculate Maximum Height:
  Subtract t =2 into the equation h(t) = -5t^2 + 20t

h(2) = -5(2)^2 + 20(2)
h(2) = -5(4) + 40
h(2) = -20 + 40 = 20 Meters

outcome:
The maximum height that the ball reached is 20 Meters and achieved at 20 seconds.

I am inviting; @dove11, @simonmwigwe, and @ruthjoe

Cc:-
@khursheedanwar