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Follow these steps to draw a parabola with the given equation: y = 22 − 4x + 1
1. Identify the Coefficients
In this case, a is 2, b is -4 and c is 1.
- a determines if the parabola opens up or down. In this case, it opens up since it’s a positive number.
- b determines the tilt or slant of the parabola.
- c is a constant term that shifts the parabola up or down.
2. Find the Vertex
The parabola’s vertex is (h,k). This is about to get really confusing, so hang in there with us: h is the x-coordinate of the vertex, and k is the vertex’s y-coordinate. Keep that in mind for the rest of this step.
Now, h = -b/2a. Plug in the values into the formula, and you get:
This means the x-coordinate of the vertex is 1. Now, find k, the y-coordinate of the vertex, by substituting h back into the original expression (ax2 + bx + c):
This makes the vertex (1, -1).
3. Determine the Axis of Symmetry
The parabola’s axis of symmetry (x = h) is a vertical line passing through the vertex, so as demonstrated above, this is x = 1.
4. Calculate the X-intercepts
You can solve it using the quadratic formula: x = -b ± √(b² – 4ac) / (2a). Substitute the values of a, b and c into the formula.
x = -(-4) ± √((-4)² – 4(2)(1)) / 2(2)
x = 4 ± √(16 – 8) / 4
Then you calculate the two x-intercepts: one for a + and one for a –.
x = 4 + (2√2) / 4 = 4 + (√2)/2
x = 4 – (2√2) / 4 = 4 + (√2)/2
So the x-intercepts are: 2 + (√2)/2 and 2 – (√2)/2.
5. Calculate the Y-intercept
To find the y-intercept, set x to 0 and solve for y.
This makes the y-intercept point is (0,1).
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