intercepts of 3x^2+6x — step-by-step solution

On the horizontal axis, y = 0: solve

3 x^{2} + 6 x = 0

1) Let's solve in

ℝ

3 x^{2} + 6 x = 0

You can factorize the expression:

3 x^{2} + 6 x

into:

x \cdot (3 x + 6)

A product is zero if and only if one of its factors is zero: we solve each factor equal to 0

⇥1.1) Let's solve in

ℝ

x = 0

⇥Solution found:

x = 0

⇥1.2) Let's solve in

ℝ

3 x + 6 = 0

⇥

3 x = -6

⇥ⓘ Both sides are divided by

3

⇥

x = - \frac{6}{3}

⇥ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

- \frac{6}{3}

-2

⇥Solution obtained:

x = -2

On the vertical axis, x = 0: calculate f(0)

⇥

3 \cdot 0^{2} + 6 \cdot 0

⇥ⓘ A product with a zero factor is zero:

3 \cdot 0

0

6 \cdot 0

0

⇥

0 + 0

⇥ⓘ Adding 0 changes nothing:

0 + 0

0

⇥

0

▶Axis intercepts:

{(-2, 0), (0, 0)}