Question content area top left

Question

Part 1
Sketch the graph of the quadratic function. Indicate the coordinates of the vertex of the graph.
y=−2x2+4x+3
Question content area bottom left
Part 1
Use the graphing tool to graph the function.

Click to
enlarge
graph
.
.
.
Question content area right
Part 1
-15
-12
-9
-6
-3
3
6
9
12
15
-15
-12
-9
-6
-3
3
6
9
12
15
x
y

Answer 1

To sketch the graph of the quadratic function y = -2x^2 + 4x + 3, you can use the following steps:

Step 1: Find the x-coordinate of the vertex using the formula x = -b/2a, where a = -2 and b = 4.

x = -4 / (2 * (-2))
x = -4 / (-4)
x = 1

Step 2: Substitute the x-coordinate of the vertex into the equation to find the y-coordinate.

y = -2(1)^2 + 4(1) + 3
y = -2 + 4 + 3
y = 5

So the vertex of the graph is (1, 5).

Step 3: Plot the vertex on the graph.

Step 4: Choose a few x-values on both sides of the vertex and substitute them into the equation to find the corresponding y-values. For example, you can choose x = -2, -1, 0, 2, and 3.

x = -2: y = -2(-2)^2 + 4(-2) + 3 = -8 - 8 + 3 = -13
x = -1: y = -2(-1)^2 + 4(-1) + 3 = -2 - 4 + 3 = -3
x = 0: y = -2(0)^2 + 4(0) + 3 = 0 + 0 + 3 = 3
x = 2: y = -2(2)^2 + 4(2) + 3 = -8 + 8 + 3 = 3
x = 3: y = -2(3)^2 + 4(3) + 3 = -18 + 12 + 3 = -3

Step 5: Plot the points obtained in Step 4 and connect them to form a smooth curve.

The sketch of the graph of the quadratic function y = -2x^2 + 4x + 3 should look like this:

|
|
|
V(1, 5)
|
|
------------------------------
|
|
|
|

Note: The vertical axis represents the y-axis and the horizontal axis represents the x-axis. The x-values are marked on the horizontal axis, and the corresponding y-values are marked on the vertical axis.