6. What are the solutions of the equation? $ x^2 - 10x + 24 = 0 $a. $ x = -1 $ or $ x = -24 $b. $ x = -4 $ or $ x = -6 $c. $ x = -1 $ or $ x = 24 $d. $ x = 4 $ or $ x = 6 $ ### Transcription and Explanation**Problem Statement:**5. Write $ y = 3(x-5)(x-6) $ in standard form and graph $ y = 3(x-5)(x-6) $.---**Given Equations and Their Standard Forms:**- **a.** $ y = 3x^2 - 11x + 30 $- **b.** $ y = 3x^2 - 11x + 30 $- **c.** $ y = 3x^2 - 33x + 90 $- **d.** $ y = 3x^2 - 33x + 90 $---**Graphs Explanation:**The document contains four graphs, indicated as a, b, c, and d, corresponding to the equations above.1. **Graph a:** - Plots the parabola $ y = 3x^2 - 11x + 30 $. - The vertex is shown below the x-axis, and it opens upwards. - The graph indicates the parabola’s intercepts, with x-intercepts at points that aren't explicitly marked.2. **Graph b:** - Shows an identical parabola to Graph a, $ y = 3x^2 - 11x + 30 $. - This suggests reinforcement of the function graphed in standard form. - Like Graph a, the parabola opens upwards.3. **Graph c:** - Displays the parabola $ y = 3x^2 - 33x + 90 $. - The vertex of this parabola is also below the x-axis. - The parabola opens upwards, consistent with the positive leading coefficient.4. **Graph d:** - Identical to Graph c, again plotting $ y = 3x^2 - 33x + 90 $. - Emphasizes the same characteristics as Graph c, with the parabola opening upwards.---**Conclusion:**The activity involves converting the given quadratic expression into a standard form and graphing it. The graphs visually illustrate the parabolic nature of quadratic functions, focusing on the forms of the equations given. Each graph exhibits the effect of the standard form coefficients on the vertex and the direction of opening of the parabola.

Answered: 6. What are the solutions of the…

6. What are the solutions of the equation? x - 10x+ 24 0 a x=-1 or x =-24 b. x= -4 or x = -6 C. X= -1 or x = 24 d. x = 4 or x 6 %3D

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

6. What are the solutions of the equation? $ x^2 - 10x + 24 = 0 $

a. $ x = -1 $ or $ x = -24 $

b. $ x = -4 $ or $ x = -6 $

c. $ x = -1 $ or $ x = 24 $

d. $ x = 4 $ or $ x = 6 $

### Transcription and Explanation

**Problem Statement:**

5. Write $ y = 3(x-5)(x-6) $ in standard form and graph $ y = 3(x-5)(x-6) $.

---

**Given Equations and Their Standard Forms:**

- **a.** $ y = 3x^2 - 11x + 30 $
- **b.** $ y = 3x^2 - 11x + 30 $
- **c.** $ y = 3x^2 - 33x + 90 $
- **d.** $ y = 3x^2 - 33x + 90 $

---

**Graphs Explanation:**

The document contains four graphs, indicated as a, b, c, and d, corresponding to the equations above.

1. **Graph a:**
- Plots the parabola $ y = 3x^2 - 11x + 30 $.
- The vertex is shown below the x-axis, and it opens upwards.
- The graph indicates the parabola’s intercepts, with x-intercepts at points that aren't explicitly marked.

2. **Graph b:**
- Shows an identical parabola to Graph a, $ y = 3x^2 - 11x + 30 $.
- This suggests reinforcement of the function graphed in standard form.
- Like Graph a, the parabola opens upwards.

3. **Graph c:**
- Displays the parabola $ y = 3x^2 - 33x + 90 $.
- The vertex of this parabola is also below the x-axis.
- The parabola opens upwards, consistent with the positive leading coefficient.

4. **Graph d:**
- Identical to Graph c, again plotting $ y = 3x^2 - 33x + 90 $.
- Emphasizes the same characteristics as Graph c, with the parabola opening upwards.

---

**Conclusion:**

The activity involves converting the given quadratic expression into a standard form and graphing it. The graphs visually illustrate the parabolic nature of quadratic functions, focusing on the forms of the equations given. Each graph exhibits the effect of the standard form coefficients on the vertex and the direction of opening of the parabola.

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