Graph the equation y, equals, minus, x, squared, minus, 2, x, plus, 3y=−x 2 −2x+3 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Question
Graph the equation y, equals, minus, x, squared, minus, 2, x, plus, 3y=−x 2 −2x+3 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Solution
Sure, here are the steps to graph the equation y = -x^2 - 2x + 3:
Step 1: Identify the vertex The vertex form of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola. The given equation is already in vertex form, so the vertex is (h, k) = (-1, 3).
Step 2: Identify the roots The roots of the equation are the x-values where y = 0. To find these, set the equation equal to zero and solve for x:
0 = -x^2 - 2x + 3 x^2 + 2x - 3 = 0 (x - 1)(x + 3) = 0 x = 1, -3
So the roots are x = 1 and x = -3.
Step 3: Choose two more points Choose two more x-values and calculate the corresponding y-values. For example, choose x = -2 and x = 2:
For x = -2, y = -(-2)^2 - 2*(-2) + 3 = -4 + 4 + 3 = 3. For x = 2, y = -(2)^2 - 2*2 + 3 = -4 - 4 + 3 = -5.
So the two additional points are (-2, 3) and (2, -5).
Step 4: Plot the points and draw the graph Plot the vertex (-1, 3), the roots (1, 0) and (-3, 0), and the two additional points (-2, 3) and (2, -5) on the graph. Draw a smooth curve through the points to complete the graph of the equation.
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