x^{2}+8x+7 What happens to the y-values as x increases and as x decreases


The given quadratic expression is:

\[
y = x^2 + 8x + 7
\]

### Behavior of the function as \(x\) increases and decreases:

1. **As \(x\) increases** (positive values of \(x\)):
   - The term \(x^2\) becomes increasingly large.
   - The linear term \(8x\) also increases but at a slower rate compared to \(x^2\).
   - As a result, the \(y\)-values increase rapidly as \(x\) increases.

2. **As \(x\) decreases** (negative values of \(x\)):
   - The quadratic term \(x^2\) still grows, but it grows positively since squaring any number gives a positive result.
   - The term \(8x\) becomes more negative (since \(x\) is negative), but the \(x^2\) term dominates for large negative values.
   - Therefore, the \(y\)-values still increase as \(x\) decreases significantly in magnitude.

### Conclusion:
- As \(x\) increases or decreases significantly, \(y\)-values grow larger due to the dominance of the \(x^2\) term. The graph of this quadratic function is a parabola opening upwards, meaning it has a minimum point (vertex) and then rises as you move in either direction away from the vertex.

Do you want further details or explanations about this? 

Here are 5 related questions:
1. What is the vertex of the quadratic function?
2. How do you find the axis of symmetry for a parabola?
3. How does the sign of the coefficient of \(x^2\) affect the direction of the parabola?
4. Can you find the roots of the quadratic equation?
5. What is the minimum value of this quadratic function?

**Tip**: The turning point of a parabola (vertex) gives useful information about where the function reaches its minimum or maximum value.

What happens to the y-values as x increases and as x decreases for the expression x^{2}+8x+7?

Explore the behavior of the y-values in the quadratic function x^2 + 8x + 7 as x increases and decreases. Learn how the function's y-values grow larger due to the dominance of the x^2 term. Suitable for students in Grades 8-10 studying quadratic equations and parabolas.

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