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7 December, 10:51

What characteristics are easily found when given a quadratic equation in Standard form and/or vertex form?

Explain exactly how you determine the characteristics. i. e. In vertex form (h, k) is the vertex of the parabola.

How do you change a quadratic equation in vertex form to standard form? ex: y = 2 (x + 3) ^2 - 1

How do you change a quadratic equation in standard form to vertex form? ex: y = x^2 + 16x + 2

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  1. 7 December, 11:57
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    Step-by-step explanation:

    a)

    y=2 (x + 3) ^2-1

    this equation is in vertex form,

    it is:

    vertically stretched by a factor of 2

    left 3 units (f (x) = a * (x - h) ^ (2) + k, so if h is positive it was - (-h) before ot got simplified)

    down 1 unit

    thus, vertex is (-3,-1)

    b)

    you can change it to standard form (f (x) = ax^ (2) + bx+c) by:

    simply multiplying everything out:

    y=2 (x + 3) ^2-1

    y=2 (x^ (2) + 6x+9) - 1

    y=2x^ (2) + 12x+18-1

    y=2x^ (2) + 12x+17

    c)

    y=x^2+16+2

    this equation is in standard form,

    you can change it to vertex form (f (x) = a * (x - h) ^ (2) + k by:

    y=1 (x-h) ^2+k

    h=-b/2a

    h=-16/2 (1)

    h=-8

    solve for k

    y=x^2+16+2

    since vertex is (h, k) lets plug in h for x to find k and just solve for y:

    k=y = (-8) ^2+16+2

    k=y=64+16+2

    k=y=82

    k=82

    now that we know the vertex, lets write the equation in vertex form:

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

    y=1 (x - (-8)) ^ (2) + 82

    y = (x+8) ^2+82
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