https://file.aiquickdraw.com/mathbot/file/17260681657661p1r1o74.jpg

The given graph represents the quadratic function:

\[
y = x^2 + x - 5
\]

To estimate the solutions to the equation:

\[
x^2 + x - 5 = 0
\]

we are looking for the points where the graph intersects the x-axis, which correspond to the roots (or zeros) of the equation.

From the graph:

- One root appears to be slightly left of \(x = -3\).
- The other root appears to be slightly right of \(x = 1.5\).

Let's estimate these values to one decimal place:

1. The first solution is approximately \(x \approx -3.7\).
2. The second solution is approximately \(x \approx 1.7\).

Thus, the approximate solutions to the equation \(x^2 + x - 5 = 0\) are:

\[
x \approx -3.7 \quad \text{and} \quad x \approx 1.7.
\]

Do you need further clarification or a more detailed breakdown?

Here are some related questions to consider:

1. What is the quadratic formula for solving \(ax^2 + bx + c = 0\)?
2. How can you verify the solutions of a quadratic equation graphically and algebraically?
3. What is the discriminant of a quadratic equation, and how does it help determine the nature of the roots?
4. How would the graph change if the equation were \(y = x^2 + x + 5\)?
5. What are the steps to factor a quadratic equation, and why might this not be possible for all quadratics?

**Tip:** Estimating solutions from graphs is useful, but always cross-check them with algebraic methods like the quadratic formula for more accuracy.

Estimate the solutions to x^2 + x - 5 = 0 using the graph of y = x^2 + x - 5. Give your answers to 1 decimal place.

Learn how to estimate the solutions of the quadratic equation x^2 + x - 5 = 0 by interpreting its graph. This step-by-step guide covers key algebraic concepts, including the quadratic equation formula and graphical root estimation, suitable for Grades 8-10 students.

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