Find a function whose graph is a parabola with vertex (7, 8) and that passes through the point. (6, −9).

1 answer:

7 0

Work backwards from vertex form. Vertex form of a quadratic equation/parabola is the following:

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

f(x) = a(x - 6)² - 9

Now, plug in the point that you're given to SOLVE FOR A. Remember that f(x) is just another way of writing y.

8 = a(1)² - 9
8 = a - 9
a = 17

So, plug in a = 17 into the equation.

<span>f(x) = 17(x - 6)² - 9 ←← your answer.

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IfA=(-2,-4) and B=(-8,4), what is the length of AB?

lisabon 2012 [21]

Answer:

<h2>10 units </h2>

solution,

A(-2,-4)--->(X1,y1)

B(-8,4)----->(x2,y2)

now,

$ab = \sqrt{(x2 - x1) ^{2} + {(y2 - y1)}^{2} } \\ \: \: \: \: = \sqrt{ (- 8 - ( - 2)) ^{2} + (4 - ( - 4)) ^{2} } \\ \: \: \: = \sqrt{( - 8 + 2) ^{2} + {(4 + 4)}^{2} } \\ \: \: \: = \sqrt{( - 6) ^{2} + {(8)}^{2} } \\ \: \: = \sqrt{36 + 64} \\ \: \: \: = \sqrt{100} \\ \: \: \: = \sqrt{ {(10)}^{2} } \\ \: \: \: \: = 10 \: units$