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:

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

$$ x^2 + 25 = 0 \implies \text{degree } 2 \implies \text{quadratic} $$

Answer:

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