Where does the following equation intercept the x axis? y=x^2+7x+12

To find where the equation intercepts the x-axis, we set \( y = 0 \), as the x-axis intercept occurs when the value of \( y \) is zero.

Given:
\[
y = x^2 + 7x + 12
\]
Set \( y = 0 \):
\[
0 = x^2 + 7x + 12
\]
Now, solve the quadratic equation by factoring.

We need two numbers that multiply to 12 and add to 7. These numbers are 3 and 4. So we can factor the equation as:
\[
0 = (x + 3)(x + 4)
\]
Now, set each factor equal to zero:
\[
x + 3 = 0 \quad \text{or} \quad x + 4 = 0
\]
Solving these gives:
\[
x = -3 \quad \text{or} \quad x = -4
\]

Thus, the equation intercepts the x-axis at \( x = -3 \) and \( x = -4 \).

Would you like further details on this? Here are five related questions for you to explore:

1. How do you factor a quadratic equation?
2. What are other methods to solve quadratic equations besides factoring?
3. How can you confirm the intercepts are correct using a graph?
4. What do the x-intercepts of a quadratic function represent geometrically?
5. How does the quadratic formula work for finding x-intercepts?

**Tip:** Factoring works best when the quadratic can be easily split into simple binomials, but when it’s hard to factor, try using the quadratic formula.

Where does the following equation intercept the x axis? y = x^2 + 7x + 12

Discover how to find the x-intercepts of the quadratic equation y = x^2 + 7x + 12 by factoring. This step-by-step guide covers factoring quadratics, applying the zero-product property, and solving for x. Ideal for students in Grades 7-9 learning key algebraic concepts.

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