Math - Grade 9

Illustration of Quadratic Equation

Examples here are not literally the same to your modules. It only provides a guide how to answer. It provides the same concept to the activities of your modules but I changes the given numbers or figures. Have fun answering your modules!

What I know?
1. Which of the following is a quadratic equation?
a. m² + 10m - 8 = 0   (quadratic eq.)
b. 4n - 5 = 0                (linear eq.)
c. z² +20z + 12    (quadratic expression)
d. 4a² + 9a > 5     (quadratic inequality)

📖The correct answer is letter a. Quadratic equation is a polynomial equation, with 2 as the highest power of the variable. Its general formula is ax² + bx + c = 0.

📙The following are not the answer because of the following reasons:
🔖Letter b is a linear equation because the highest power of the variable n is 1.
🔖Letter c is a quadratic expression not an equation. It will become an equation if it is equal to any number.
🔖Letter d is a quadratic inequality. Note that it uses greater than instead of equal.

2. In the quadratic equation 4m² + 10m + 8 = 0, which is the quadratic term?

📖 The correct answer is 4m².
🔖 10m is the linear term.
🔖 8 is the constant term
🔖 m² is only the variable, not the term.

3. What is the standard form of the equation?

📖 The standard form is ax² + bx + c = 0.

4. Note:
📖 ax² + bx + c = 0 is a quadratic equation.
🔖ax² + bx + c > is an example of a quadratic inequality.
🔖ax + by = c is a linear equation.
🔖ax + by > c is an example of linear inequality.

Cut. Some of the items follow the same concept of the previous items.

8. In the quadratic equation, 7 - 8w = 20w², note that its standard form is 20w² + 8w -7 = 0. (Hint: Rewrite the equation into its standard form).
It follows:
ax² = 20w².   📖Therefore, a = 20
bx = 8w.        📖 Therefore, b = 8
c = -7.             📖Therefore, c = -7

9. Transform the equation q(q-10) = 2
to the quadratic equation in the form of
ax² + bx + c = 0.

Step 1. Solve the left hand side of the equation.
q(q-10) = q² - 10q
Note that the equation now will be
q² - 10q = 2

Step 2. Add -2 to the both sides of the equation.
q² - 10q -2 = 2 -2

Step 3. Simplify the equation.
             📖q² - 10q - 2 = 0

10. The length of a rectangular swimming pool is 50m longer than its width and its area is 400m². If w represents the width of the swimming pool, how would you represent its length?

Step 1. Note that w represents the width.

Step 2. Note that the length is 50m longer than its width, it follows:
length = w + 50
📖 The length is w + 50.

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Finally, part 1 is finished. Now, follow the examples above and I'm sure you can get a perfect score🏅. I know you can do it!
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