**Q: Graph the Quadratic Function: f(x) = 2x**^{2 }– 3x + 1

Answer:

There are two main methods to do this. I will do both methods (depending on what you have learned in class, you will want to pick either method 1 or method 2 that I show).

**Method 1: Plotting Points**

Because this is a quadratic equation, we know the graph will be in the shape of a parabola. So, I am going to pick a few values for x, then find the y values. Then, I will plot the points on the graph to make a parabola. You can pick any values for x when you do this method.

Let’s pick x = 0. So, plug x into the equation to find y:

**2(0)**^{2 }– 3(0) + 1 = 0 – 0 + 1 = 1

**Point 1: When x = 0, y = 1: (0, 1)**

Let’s pick x = 1 now:

**2(1)**^{2 }– 3(1) + 1= 2(1) – 3 + 1 = 2 – 3 + 1 = 0

**Point 2: When x = 1, y = 0: (1, 0)**

Let’s pick x = -1 now:

**2(-1)**^{2 }– 3(-1) + 1= 2(1) + 3 + 1 = 2 + 3 + 1 = 6

**Point 3: When x = -1, y = 6: (-1, 6)**

Now, plot the points (0, 1) and (1, 0) and (-1, 6) on a graph. Connect the dots to make a parabola!

Keep in mind: You may need to get more than 3 points for better accuracy.

**Method 2: Finding the y-intercept and the vertex:**

The y-intercept of **any **type of graph occurs when you plug in 0 for x. So, plug in 0 for x into the equation and solve for y:

Continue reading Graphing a Quadratic Function: 2 methods

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