a To graph y=x^2 we will first calculate some points in a value table.
|c|c|c|
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x& x^2 & y [0.2em]
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-4 & ( -4)^2 & 16 [0.2em]
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-3 & ( -3)^2 & 9 [0.2em]
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-2 & ( -2)^2 & 4 [0.2em]
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-1 & ( -1)^2 & 1 [0.2em]
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0 & 0^2 & 0 [0.2em]
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1 & 1^2 & 1 [0.2em]
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2 & 2^2 & 4 [0.2em]
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3 & 3^2 & 9 [0.2em]
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4 & 4^2 & 16 [0.2em]
Now we can graph the parabola. We will also draw a line through the points where the x-coordinate is -4 and 2.
To write the equation in slope-intercept form, we need to know the line's slope m and its y-intercept b.
y=mx+b
From the diagram, we can identify the y-intercept as b=8. To find the slope, we will substitute the two points into the Slope Formula and evaluate.
Notice that we could also measure the obtuse angle that the line makes with the x-axis. Let's call this angle α.
Notice that ∠θ and ∠α make a Linear Pair which means they sum to 180^(∘). With this information, we can solve for ∠α.
63.4^(∘)+ m ∠α = 180^(∘)
⇕
m∠α = 116.6^(∘)
