SLC-S22W4//Linear and Quadratic equations equations

I'm so delighted to be a part of this contest, here is my own contribution to the lesson that was taught.

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Task 1

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

Linear Equations

A linear equation has the highest power of variable 1.

• General Form: ax + b = 0; where a ≠ 0

• Example: 2x + 3 = 5

Quadratic Equations

A quadratic equation has the highest power of variable 2.

• General Form: ax² + bx + c = 0; where a ≠ 0

• Example: x² + 4x + 4 = 0

Common Differences

• Linear Equations: When plotted on a graph, they form straight lines.

• Quadratic Equations: When plotted on a graph, they form parabolas.

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Task 2

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

Factoring Method

Involves simplifying the quadratic equations by splitting them into two binomials.

• Pros: It is a simple method for solving if the equation can be factored without difficulty.

• Cons: It cannot be applied if the equation cannot be easily factored.

Quadratic Formula Method

Formula: x = –b ± √(b² – 4ac) / 2a

• Pros: It is applicable to all quadratic equations.

• Cons: In cases of large numbers, it may involve complex calculations.

Graphical Method

It involves plotting the graph for the quadratic equations to find the x-intercept.

• Pros: This concept gives a visual representation of the equation.

• Cons: It requires the use of graphical tools, and the solution may not be exact.

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Task 3

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

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

(You are required to solve these problems at paper and then share clear photographs for adding a touch of your creativity and personal effort which should be marked with your username)

_{Shot with my device}

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Task 4

Scenario number 1

Suppose Ali have $15 for spending at snacks. He is buying a pack of chips for $3. How much money he have left?

Suppose x is amount of money Ali has left.

Equation: x + 3 = 15

Share a solution for x

(Solve the above scenerio based questions and share step by step that how you reach to your final outcome)

Scenario number 2

Suppose there's a ball which is thrown in upward direction from ground with initial velocity of 20 m/s and height of ball above ground is presented by following equation;

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

Here h is height in meters and t is time in seconds.

Share about maximum height reached by this ball!

Please solve for h!

Scenario 1: Money left with Ali

Given equation: x + 3 = 15

Solution
x + 3 = 15
Subtract 3 from both sides
x + 3 – 3 = 15 – 3
→ x = 12
What Ali will have left is $12.

Scenario 2: Maximum Height of Ball

Given equation: h(t) = –5t² + 20t

Solution
Firstly, we will find the maximum curvature of the parabola (vertex).
Using: t = –b / 2a
Where: a = –5, b = 20

Then: t = –20 / 2(–5)
t = –20 / –10
Therefore: t = 2

Substitute t = 2 into the given equation
h(2) = –5(2)² + 20(2)
h(2) = –20 + 40
h(2) = 20

Maximum height reached by the ball is 20 meters.

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I will invite;

@imohmitch
@us-andrew
@precious9

Cc,
@khursheedanwar