Pre-calc

1. Find the equation for a quadratic function whose vertex is (2,5) and whose graph contains the point (-8,15).

2.What are the x- and y- intercepts for y=2x^2+x-6

Plesee explai. I want to learn to learn how to do them.

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  1. The standard form of a quadratic is

    y = a(x-h)^2 + k, where (h,k) is the vertex.

    since we know the vertex we can start with

    y = a(x-2)^2 + 5 , leaving us only with the a as an unknown, but we know the point (-8,15) lies on it, thus must satisfy our equation, so ...

    15 = a(-8-2)^2 + 5
    10 = 100a
    a = 10/100 = 1/10

    equation: y = (1/10)(x-2)^2 + 5

    2.

    for the y-intercept, let x = 0
    we can visually see the would give us y = 6

    for the x-intercept, let y = 0
    then
    2x^2 + x - 6 = 0
    (2x - 3)(x + 2) = 0
    x = 3/2 or x = -2

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