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Klio2033 [76]
3 years ago
8

Write the equation for the quadratic function in standard form

Mathematics
1 answer:
Ede4ka [16]3 years ago
8 0

Answer:

y=x^2+6x+7

Step-by-step explanation:

To write the quadratic in standard form, begin by writing it in vertex form

y = a(x-h)^2+k

Where (h,k) is the vertex of the parabola.

Here the vertex is (-3,-2). Substitute and write:

y=a(x--3)^2+-2\\y=a(x+3)^2-2

To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,7) a y-intercept of the parabola.

7=a((0)+3)^2-2\\7=a(3)^2-2\\7=9a-2\\9=9a\\1=a

The vertex form of the equation is y=(x+3)^2-2.

To write in standard form, convert vertex form through the distributive property.

y=(x+3)^2-2\\y=(x^2+6x+9)-2\\y=x^2+6x+7

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