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To find the standard form of the parabola equation, we need to expand the equation and simplify it.
Starting with the given equation:
y = ¼(x² – 2x + 5)
First, let’s distribute the ¼ to the terms inside the parentheses:
y = ¼ × x² – ¼ × 2x + ¼ × 5
Simplifying further:
y = ¼x² – ½x + 5/4
Next, we need to get rid of the fractions by multiplying the entire equation by 4 to eliminate the denominators:
4y = 4 × (¼x² – ½x + 5/4)
Resulting in:
4y = x² – 2x + 5/4
To convert this into standard form, we can move all the terms to one side of the equation:
x² – 2x + 5/4 – 4y = 0
Since the standard form of a parabola equation is y = ax² + bx + c, we need to rearrange the terms further.
To do this, let’s multiply the entire equation by 4 to eliminate fractions and simplify:
4x² – 8x + 5 – 16y = 0
Finally, we can write the standard form of the parabola equation:
4x² – 8x – 16y + 5 = 0
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Find the standard form parabola equation.
y=¼(x²-2x+5)
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