GRAPHING QUADRATIC EQUATIONS PART 1

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This lesson will show the basics behind graphing quadratic equations.

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Consider this quadratic equation, y = x^2 -4.

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Now, from this table, we can see that all the x-coordinates are given.

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To graph the equation, we can use these x-coordinates to find all the y-coordinates.

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After doing so, we will have the coordinates of seven points that can be used to graph the equation.

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Let's start. When x is -3, we can substitute x in this equation with -3.

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Now, let's simplify this equation. (-3)^2 square, is the same as -3, multiply by -3, which equals to 9.

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Let's write this back here. 9 minus 4, gives 5. Hence, we get y equals to 5.

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Now, let's fill in this box with 5.

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With this, we have a point with the coordinates (-3, 5). This point is located right over here.

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Let's calculate the next point. Substituting x, with --2. (-2)^2 is the same as -2, multiply by -2, which is equals to 4.

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Let's write this number here.

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Next, 4 subtract by 4, gives 0. Hence, we have y equals to 0.

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Now, we can write the number 0, here.

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By doing so, we get a point with the coordinates (-2, 0). This point is located right over here.

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To find the next point, we repeat the same steps as before. Substitute x in this equation with -1.

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Simplifying (-1)^2, gives 1. 1 minus 4 gives, -3. Hence, we have y equals to -3. Now, let's fill in this box with -3.

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With this, we have a point with the coordinate (-1, -3), and this point is located right over here.

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Now, by repeating the same steps for the rest of the x-coordinates, we will have all the y coordinates.

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The point with the coordinates (0, -4) is located here. Next, the point with the coordinates (1, -3) is located here. Again, the point with the coordinates (2, 0) is located here. Finally, the point with the coordinates (3, 5) is located here.

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Now, we have 7 points. By drawing a curve shown here, we can join these points together. This gives the quadratic equation, y = x^2 -4

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That is all for this lesson. In the next lesson, we will learn about the vertex of a quadratic graph.

GRAPHING QUADRATIC EQUATIONS PART 2

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In this lesson, we will learn another way for graphing quadratic equations.

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Consider this quadratic equation, y = -x^2+2x+4.

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First, we need a table to record the coordinates of the points that we are going to calculate.

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Since the x-coordinates are not given in this table, we need a way to get them.

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To do so, we can use the formula for the x-coordinate of the vertex of a quadratic equation, x = -b/2a.

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To find the values of 'a' and ‘b', we can compare this equation with the general quadratic equation, y = ax^2 + bx +c.

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For easier comparison, we can rewrite this equation as, y = -1x^2 +2x +4.

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By comparing, we have, a=-1, b=2, and c=4.

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Knowing this, we can substitute 'a' with -1, and substitute 'b' with 2.

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Let's simplify this term. Now, this term is the same as, -2/2(-1). 2 multiply by -1, gives -2. -2 divides by -2, gives 1.

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Hence, we have, x=1. Let's write this down here.

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With this, we know that we have a point with the x-coordinate of 1, and this point is located at the middle of the graph.

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Keeping this in mind, we can pick the rest of the x-coordinates, by taking three x-coordinates smaller than 1, which are, 0, -1, -2. And take three x-coordinates greater than 1, which are 2, 3, and 4.

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Let's change back to the original equation. With all the x-coordinates, we can now use this equation to calculate the y-coordinates. Here’s how.

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When the x-coordinate is -2, we can substitute x in this term with -2. Similarly, we can substitute x in this term with -2. Let's calculate for y. 2 multiply with -2, gives -4. -4 and +4, cancels off each other.

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(-2)^2, is the same as, -2 multiply by -2. which is equals to 4. Let's write this down here.

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So now, we have, y equals to -4. Let's write it here.

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We can perform the same steps to find the rest of the y-coordinates.

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After doing so, the table will be filled with numbers as shown.

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Alright, let's put these points on the graph.

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The point (-2, -4) is located here.

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The point (-1, 1) is located here.

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The point (0, 4) is located here.

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Now, we repeat the same steps with the rest of the coordinates, and we will have all the points in placed, as seen on the graph.

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Finally, we draw a curve to join these points together, as shown.

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This is the graph of y=-x^2+2x+4.

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That is all for this lesson, try out the practice question to test your understanding

--End of Transcript for Graphing Quadratic Equations 2--