Question

when a golfer strikes a ball with the club, the ball travels along a parabolic path.

the parabolic path can be modeled by a quadratic equation.

quadratic equation

a quadratic equation is an equation where the highest exponent of the variable is 2.

the standard form of the quadratic equation is written as:

(ax^2 + bx + c = 0)

where (a), (b), and (c) are real numbers and (a \
eq 0).

examples

(5x^2 - 3x + 12 = 0)

(x^2 + 9 = 0)

(2x^2 + 7x - 5 = 0)

value: 3

identify the quadratic equations from the following.

mark all correct answers

a. (2x^2 + 5x - 6 = 0)
b. ((x - 2)(x + 3)(x + 1) = 0)
c. (3x^2 - 99 = 0)
d. (4x^2 + 3x^3 + 5x - 8 = 1)
e. (x^2 + 25 = 0)

Explanation:

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<reasoning>

Define a quadratic equation

Using the Quadratic Equations knowledge point
\[
ax^2 + bx + c = 0, \quad a
e 0
\]

Analyze option a

Using the Quadratic Equations knowledge point
\[
2x^2 + 5x - 6 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]

Analyze option b

Using the Quadratic Equations knowledge point
\[
(x - 2)(x + 3)(x + 1) = 0 \implies \text{degree } 3 \implies \text{not quadratic}
\]

Analyze option c

Using the Quadratic Equations knowledge point
\[
3x^2 - 99 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]

Analyze option d

Using the Quadratic Equations knowledge point
\[
4x^2 + 3x^3 + 5x - 8 = 1 \implies \text{degree } 3 \implies \text{not quadratic}
\]

Analyze option e

Using the Quadratic Equations knowledge point
\[
x^2 + 25 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]
</reasoning>

<answer>
<mcq-correct>(a) \(2x^2 + 5x - 6 = 0\)</mcq-correct>
<mcq-option>(b) \((x - 2)(x + 3)(x + 1) = 0\)</mcq-option>
<mcq-correct>(c) \(3x^2 - 99 = 0\)</mcq-correct>
<mcq-option>(d) \(4x^2 + 3x^3 + 5x - 8 = 1\)</mcq-option>
<mcq-correct>(e) \(x^2 + 25 = 0\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Define a quadratic equation

Using the Quadratic Equations knowledge point
\[
ax^2 + bx + c = 0, \quad a
e 0
\]

Analyze option a

Using the Quadratic Equations knowledge point
\[
2x^2 + 5x - 6 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]

Analyze option b

Using the Quadratic Equations knowledge point
\[
(x - 2)(x + 3)(x + 1) = 0 \implies \text{degree } 3 \implies \text{not quadratic}
\]

Analyze option c

Using the Quadratic Equations knowledge point
\[
3x^2 - 99 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]

Analyze option d

Using the Quadratic Equations knowledge point
\[
4x^2 + 3x^3 + 5x - 8 = 1 \implies \text{degree } 3 \implies \text{not quadratic}
\]

Analyze option e

Using the Quadratic Equations knowledge point
\[
x^2 + 25 = 0 \implies \text{degree } 2 \implies \text{quadratic}
\]
</reasoning>

<answer>
<mcq-correct>(a) \(2x^2 + 5x - 6 = 0\)</mcq-correct>
<mcq-option>(b) \((x - 2)(x + 3)(x + 1) = 0\)</mcq-option>
<mcq-correct>(c) \(3x^2 - 99 = 0\)</mcq-correct>
<mcq-option>(d) \(4x^2 + 3x^3 + 5x - 8 = 1\)</mcq-option>
<mcq-correct>(e) \(x^2 + 25 = 0\)</mcq-correct>
</answer>

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