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Anni [7]
3 years ago
7

How do you solve a question algbraically

Mathematics
1 answer:
Julli [10]3 years ago
3 0

Answer:

Step 1: Multiply the entire first equation by 2.

Step 2: Rewrite the system of equations, replacing the first equation with the new equation.

Step 3: Add the equations.

Step 4: Solve for x.

Step 5: Find the y-value by substituting in 3 for x in either equation.

Step 6: Identify the solution as an ordered pair.

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Derive the equation of the parabola with the focus <br> is (-7,5) and the directrix of y=-11
Volgvan
So, notice, the focus point is at -7, 5, and the directrix is at y = -11.

keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.

with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.

since the parabola is opening upwards, "p" is positive 8.

\bf \textit{parabola vertex form with focus point distance}\\\\&#10;\begin{array}{llll}&#10;4p(x- h)=(y- k)^2&#10;\\\\&#10;\boxed{4p(y- k)=(x- h)^2}&#10;\end{array}&#10;\qquad &#10;\begin{array}{llll}&#10;vertex\ ( h, k)\\\\&#10; p=\textit{distance from vertex to }\\&#10;\qquad \textit{ focus or directrix}&#10;\end{array}\\\\&#10;-------------------------------\\\\&#10;\begin{cases}&#10;h=-7\\&#10;k=-3\\&#10;p=8&#10;\end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2&#10;\\\\\\&#10;32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2&#10;\\\\\\&#10;y=\cfrac{1}{32}(x+7)^2-3

8 0
2 years ago
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