Y=2x²-10
To prepare for your university exams, it's important to understand how to work with equations and functions. Let's analyze the equation y = 2x² - 10.
This equation represents a quadratic function, where the highest power of x is 2. The general form of a quadratic function is y = ax² + bx + c. In your equation, a = 2, b = 0, and c = -10.
To better understand this quadratic function, you can analyze its properties:
Vertex: The vertex of a quadratic function represents its minimum or maximum point on the graph. The x-coordinate of the vertex can be found using the formula x = -b / (2a). In this case, since b = 0, the x-coordinate is x = 0. To find the y-coordinate, substitute x = 0 into the equation: y = 2(0)² - 10. Thus, the vertex is (0, -10).
Axis of Symmetry: The axis of symmetry is the vertical line that passes through the vertex. In this case, the axis of symmetry is x = 0.
y-Intercept: The y-intercept is the point where the graph intersects the y-axis. It can be found by setting x = 0 in the equation: y = 2(0)² - 10. Therefore, the y-intercept is (0, -10).
x-Intercepts: The x-intercepts are the points where the graph intersects the x-axis. To find them, set y = 0 and solve for x. In this case, we have 0 = 2x² - 10. Adding 10 to both sides, we get 10 = 2x². Dividing both sides by 2, we have 5 = x². Taking the square root of both sides, we get x = ±√5. Therefore, the x-intercepts are (√5, 0) and (-√5, 0).
Graph Shape: Since the coefficient of the x² term is positive (2), the parabola opens upwards. This means the graph will have a minimum point at the vertex (0, -10) and will be concave upward.
It's also useful to evaluate the function at specific x-values or to find the derivative for more advanced analysis. Remember to practice solving similar equations and understanding the properties of different types of functions, as this will help you in your university exams.
