The given equation (x - 2)² - 3 is in standard form x² - 4x - 2. To graph y = -(x+3)² + 3, find the vertex (-3, 3) and plot points on either side. For y = x² - 6x + 5, the vertex is (3, -4) and the parabola opens upward.
Step-by-step explanation:
The given equation (x − 2)² − 3 can be expanded and simplified to x² - 4x + 1. To put it in standard form, we arrange the terms in descending order of the degree of x. So the standard form of the equation is x² - 4x + 1 - 3 = x² - 4x - 2.
To graph the equation y = -(x+3)² + 3, we start by finding the vertex, which is (-3, 3) because the equation is in the vertex form y = a(x-h)² + k. The negative value of a indicates a downward opening parabola. We can plot points on either side of the vertex and draw a smooth curve passing through these points.
To graph the equation y = x² - 6x + 5, we first rewrite it as y = (x - 3)² - 4. The vertex is (3, -4) and the parabola opens upward. By plotting points on either side of the vertex, we can draw the graph.