Someone please help me with these 2 problems :(

Mathematics

1 answer:

k0ka [10]3 years ago

7 0

If the discriminant b^2-4ac is 0, then you have TWO EQUAL, REAL ROOTS.

If you're given the x-intercepts, you can determine the factors of the polynomial as follows: Take -3, change the sign and write (x+3). Take 5, change the sign and write (x-5). Then the eq'n of the parabola is

f(x) = (x+3)(x-5) = x^2 - 2x -15, in which a=1, b = -2 and c= -15.

You can find the x-coordinate of the vertex, which is also the equation of the axis of symmetry, using

x= -b / (2a). Here, x = -(-2) / (2[1]), or x = 1

Find the y-coordinate by subbing 1 for x in the equation above:

y = (1)^2 - 2(1) - 15 = 1 - 2 - 15 = -16

The vertex is at (1, -16) and the equation of the axis of symm. is x = 1.

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A student was asked to find the slope of the line through the points (4,8) and (-3,5). His answer, <img src="https://tex.z-dn.ne

evablogger [386]

Answer:

$m=\frac{-3}{-7}$

Step-by-step explanation:

Given the following question:

Point A = (4, 8) = (x1, y1)
Point B = (-3, 5) = (x2, y2)

In order to find the slope any two points given we use the formula to find slope or rise/run.

$m=\frac{y2-y1}{x2-x1}$
$m=\frac{5-8}{-3-4} =\frac{-3}{-7}$
$m=\frac{-3}{-7}$

The reason why the students answer is incorrect because he substituted incorrectly. More specifically the run part of the formula for slope. The formula for slope goes x2 - x1 which means it should be -3 - 4, not -4 - 3, which will give you the answer -7.

Hope this helps.