Y=2x²-10

Question 1

Задача Задача №84256

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Аноним

04 декабря 2023 16:26 · публичный вопрос

А

Аноним 04 декабря 2023 16:26

Y=2x²-10

Answer

The given equation is y = 2x² - 10. To prepare for your university exams, here are several steps you can take to work with this equation:

Plot the graph: To get a visual representation of the equation, plot points on a graph. Choose different values for x and calculate the corresponding y values. Plot the points on the graph and connect them to form a parabolic curve.
Find the vertex: The vertex of a parabola can help you understand the basic shape and direction of the graph. To find the vertex, use the formula x = -b / 2a, where a and b are the coefficients of x² and x respectively. In this case, a = 2, b = 0, so the x-coordinate of the vertex is x = -0 / (2 * 2) = 0. Substitute this value of x into the equation to find the y-coordinate.
Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the equation is y = 2x² - 10, which is a symmetric equation with respect to the y-axis. Therefore, the axis of symmetry is the y-axis (x = 0).
Find the y-intercept: To find the y-intercept, substitute x = 0 into the equation. In this case, y = 2(0)² - 10 = -10. So, the y-intercept is the point (0, -10).
Find the x-intercepts (if any): To find the x-intercepts, set y = 0 and solve for x. In this case, 2x² - 10 = 0. Use factoring, completing the square, or the quadratic formula to solve for x.
Determine the symmetry of the graph: Since the equation is y = 2x² - 10, it is a symmetric equation with respect to the y-axis. This means that if you reflect the graph across the y-axis, it will look the same.
Analyze the graph: Look at the shape of the graph to understand how it behaves. In this case, the coefficient of x² is 2, which means the parabola opens upwards. The vertex is at (0, -10), and the y-intercept is at (0, -10). The x-intercepts (if any) will depend on the solutions found in step 5.
Use the graph to solve related problems: Once you have a good understanding of the graph and its properties, you can use it to solve problems related to the equation. For example, you can find the maximum or minimum values, find the range or domain, or determine the intervals where the equation is positive or negative.

Remember to practice solving similar equations and graphing them to build your understanding and confidence. Good luck with your university exams!

Question 2

y=2x²-10

Answer

The given equation is y = 2x² - 10. To prepare for your university exams, here are several steps you can take to work with this equation: 1. Plot the graph: To get a visual representation of the equation, plot points on a graph. Choose different values for x and calculate the corresponding y values. Plot the points on the graph and connect them to form a parabolic curve. 2. Find the vertex: The vertex of a parabola can help you understand the basic shape and direction of the graph. To find the vertex, use the formula x = -b / 2a, where a and b are the coefficients of x² and x respectively. In this case, a = 2, b = 0, so the x-coordinate of the vertex is x = -0 / (2 * 2) = 0. Substitute this value of x into the equation to find the y-coordinate. 3. Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the equation is y = 2x² - 10, which is a symmetric equation with respect to the y-axis. Therefore, the axis of symmetry is the y-axis (x = 0). 4. Find the y-intercept: To find the y-intercept, substitute x = 0 into the equation. In this case, y = 2(0)² - 10 = -10. So, the y-intercept is the point (0, -10). 5. Find the x-intercepts (if any): To find the x-intercepts, set y = 0 and solve for x. In this case, 2x² - 10 = 0. Use factoring, completing the square, or the quadratic formula to solve for x. 6. Determine the symmetry of the graph: Since the equation is y = 2x² - 10, it is a symmetric equation with respect to the y-axis. This means that if you reflect the graph across the y-axis, it will look the same. 7. Analyze the graph: Look at the shape of the graph to understand how it behaves. In this case, the coefficient of x² is 2, which means the parabola opens upwards. The vertex is at (0, -10), and the y-intercept is at (0, -10). The x-intercepts (if any) will depend on the solutions found in step 5. 8. Use the graph to solve related problems: Once you have a good understanding of the graph and its properties, you can use it to solve problems related to the equation. For example, you can find the maximum or minimum values, find the range or domain, or determine the intervals where the equation is positive or negative. Remember to practice solving similar equations and graphing them to build your understanding and confidence. Good luck with your university exams!