shley recently opened a store that sells only natural ingredients. She wants to advertise her products by distributing bags of s
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Hello!
The directrix of a parabola is a fixed line used in describing a curve or surface.
The standard form a parabola is 4p(x - h) = (y - k)². In this equation, h, k is the vertex, and p is the focal point.
To find the standard form, first, we would find p.
Since the equation given, y² = -24x, has a vertex at (0, 0), h, k would be zero. In this case, we can find p now.
4p = -24 (divide both sides by 4)
p = -6
4(-6)(x - 0) = (y - 0)² which can be simplified to: 4(-6)(x) = y².
Looking at the graph of the parabola, it is symmetric around the x-axis, so therefore, the directrix is a line parallel to the y-axis. To find the directrix, use the formula: x = 0 - p, and we know that p = -6.
x = 0 - (-6)
x = 6
Therefore, the directrix of the parabola is choice D, x = 6.
The expression we have is:
Step 1. Use the binomial square formula:
Applying this formula to the first binomial squared:
Step 2. Apply the formula for the square of a binomial to the second binomial:
In this case, we have some operations to solve before we move on to isolating x. So we solve the operations:
Step 3. Move the terms that are not x squared to the right side of the expression. Remember that when we move one term from one side of the equation to the other, the term must change its sign. We get the following:
Step 4. Combine like terms and arrange terms in order from the greatest exponent to the lowest and leave the independent term at the end:
And that is the final result, which is option A.
Answer: Option A.