Question

Graph the parabola. y=2x ^2 −8x+3 Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex, Then click on the graph-a-function button.

Answer 1

To graph the parabola y=2x^2-8x+3, find the vertex by completing the square, which is (2, -5). Select and calculate four more points: two to the left (1, -3) and (0, 3), and two to the right (3, -1) and (4, 3) of the vertex. Plot these on a coordinate plane and connect them with a smooth curve.

Step-by-step explanation:

To graph the parabola described by the equation y=2x^2−8x+3, we first need to determine its vertex. The vertex form of a parabola's equation is y=a(x-h)^2+k, where (h, k) is the vertex. To find the vertex for our equation, we complete the square:

y=2(x^2-4x)+3
=2(x^2-4x+4)-8+3
=2(x-2)^2-5

So, the vertex is at (2, -5). Now we will select two points to the left and two points to the right of the vertex, and find the corresponding y values.

• For x = 1: y = 2(1)^2−8(1)+3 = -3
• For x = 0: y = 2(0)^2−8(0)+3 = 3
• For x = 3: y = 2(3)^2−8(3)+3 = -1
• For x = 4: y = 2(4)^2−8(4)+3 = 3

Plot the vertex (2, -5) and the four additional points (1, -3), (0, 3), (3, -1), and (4, 3) on a coordinate plane. Connect these points with a smooth curve to visualize the parabola.