A line passes through the point (-4,6) and has a slope of -5. Write an equation in point-slope form for this line.

Mathematics

1 answer:

Art [367]2 years ago

8 0

Answer:

hope this helps you

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Answer:

The y-intercept is (0,1). The x values at the horiz. intercepts are:

{ (-3+√5)/2, (-3-√5)/2 }. Graph is that of a parabola that opens down.

Step-by-step explanation:

It'd be helpful to rewrite f(x) = 3-x2+3x-2 with the powers of x in descending order and using " ^ " to denote exponentiation:

f(x) = -x^2 + 3x -2 + 3, or

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

y-intercept: let x = 0. Then f(0) = 1. The y-intercept is (0,1)

x-intercepts: let y = f(x) = 0 = -x^2 + 3x + 1. Let's use the quadratic formula with a = -1, b = 3 and c = 1 to determine the roots of this polynomial. The discriminant, b^2-4ac, is 9-4(1)(1), or 5.

Thus, there are two real, unequal roots. They are:

-3 plus or minus √5

x = ---------------------------------

or { (-3+√5)/2, (-3-√5)/2 }

These are your two horizontal intercepts, where the function is zero.

Because the coefficient -1 of the x^2 term is negative, the parabola representing this function opens down.

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