91影视

In the given exercise, we are dealing with the vertex form of a parabola. This form is given by the equation: y = a(x-h)^2 + k . Let's break down what each part means: * **y**: This represents the value you get after performing the operations on x. * **(x-h)**: This is the horizontal translation. We subtract h from x; h is the x-coordinate of the vertex. * **k**: This is the vertical translation. We add k to the squared term; k is the y-coordinate of the vertex. * **a**: This affects the direction and how 鈥渟queezed鈥� or 鈥渟tretched鈥� the parabola is. In the problem, the equation given was y=(x-2)^2+3 . From this, we identify: * a = 1 * h = 2 * k = 3 Thus, the vertex of the parabola is at (2, 3). This tells us the highest or lowest point of the parabola and it is key to graphing the parabola accurately.

Next, we should understand the direction in which the parabola opens. In the vertex form: y = a(x-h)^2 + k, the coefficient a determines this. * If **a > 0**: The parabola opens upwards. * If **a < 0**: The parabola opens downwards. In the exercise, a is 1, which is greater than 0, indicating that the parabola opens upwards. This upwards opening tells you that the vertex is the lowest point on the graph. If a had been negative, the vertex would be the highest point.

To sketch the graph accurately, we need additional points aside from the vertex. Here's how you can calculate these points: 1. **Choose x-values around the vertex**: Pick x-values close to the x-coordinate of the vertex. 2. **Calculate corresponding y-values**: Substitute these x-values into the equation to find the corresponding y-values. In the exercise, we used x = 1 and x = 3. Let's calculate: * For **x = 1**: y = (1-2)^2 + 3 = 1 + 3 = 4. So, the point (1, 4) lies on the parabola. * For **x = 3**: y = (3-2)^2 + 3 = 1 + 3 = 4. So, the point (3, 4) lies on the parabola. You can now plot the points: * (2, 3) - the vertex * (1, 4) * (3,4) Once plotted, draw a smooth curve through these points, ensuring the curve is symmetrical around the vertex.