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zepelin [54]
3 years ago
11

Write a quadratic equation in standard form that has a vertex of (-2, 6) and passes through (-4, -2).

Mathematics
1 answer:
Marizza181 [45]3 years ago
7 0

Answer:

The equation of the quadratic in standard form is:

y=-2x^2-8x-2

Step-by-step explanation:

Since they give us the information about where the vertex of the parabola is located, and one extra points where it passes through, we can use the general form of a quadratic in vertex form:

y-y_v=a\,(x-x_v)^2

where (x_v,y_v) is the location of the vertex (in our case the point (-2,6).

Therefore the equation above becomes:

y-y_v=a\,(x-x_v)^2\\y-6=a\,(x-(-2))^2\\y-6=a\,(x+2)^2

Now,we can use the fact that the point (-4,-2) is also a point of the graph, to find the value of the parameter "a":

y-6=a\,(x+2)^2\\-2-6=a\,(-4+2)^2\\-8=a\,(-2)^2\\-8=a\,*4\\a=-2

Then, the equation of the quadratic with such characteristics becomes:

y-6=-2\,(x+2)^2\\y-6=-2x^2-8x-8\\y=-2x^2-8x-2

which is the equation of the quadratic in standard form.

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