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3 years ago

For all functions of the form f(x) = ax^2 + bx + c, which is true when b=0

Mathematics

1 answer:

Ainat [17]3 years ago

8 0

Answer:

The y-intercept will always be the vertex of the function.

Step-by-step explanation:

The functions with the following form $f(x) = ax^2 + bx + c$ are quadratic equations and have a parabolic form, which means the have a vertex. The x coordinate of the vertex is given by the following expression $x = \frac{-b}{2*a}$ . When b is equal to zero, the vertex of the function will always be the y-intercept, therefore the correct answer is the third one.

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Given the function f(x)= 14x^2 + 5x - 1 answer the question if you could change the 14 to any other number, but the rest has to

polet [3.4K]

This is a polynomial of degree 2, and remember that complex roots always come in pairs; therefore, in a second degree polynomial you can only have 0 real roots and 2 complex roots, or 2 real roots and 0 complex roots. There is no way you can have 1 real root and 1 complex root because, as stated before, complex (non-real) roots always come in pairs; so the only way of having 1 real root is dumping the polynomial of degree 2 ( $14 x^{2}$ ) by changing the 14 to 0. That way we'll left with $f(x)=5x-1$ which only has one real root:
$0=5x-1$
$5x=1$
$x= \frac{1}{5}$

7 0

3 years ago

Read 2 more answers

Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per m

docker41 [41]

Hi There!

Dori leaves her house at 12pm.

50 steps per minute until 12:20pm.

Dori has a 20 minute advantage over Malory, find the amount of steps she is ahead by,

12 - 12:20pm. steps = 20 minutes = 20 x 50 = 1000 steps

Malory leaves her house at 12:20pm.

Walks 90 steps per minute.

12:20 - 12:30 pm. = 10 minutes = 10 x 90 = 900

Dori 12:20 - 12:30pm. = 10 minutes = 10 x 50 = 500

500 + 1000 = 1500

Mallory 12:30 - 12:40 = 10 minutes = 10 x 90 = 900

900 + 900 = 1800

Dori 12:30 - 12:45pm. = 15 minutes = 15 x 50 = 500

1750 + 500 = 2250

Mallory 12:40 - 12:45pm. = 5 minutes = 10 x 90 = 900

450 + 1800 = 2250

Answer: they have the same number steps at 12:45 p.m.

Hope This Helps :)

3 0

3 years ago

In parallelogram DEFG if m_DEF=110° find m_FGD.<br> E<br> 110°<br> D<br> G

Sergio039 [100]

Answer:

E=x

or 110= x ( opposite angles of parallelogram are congurent)

E+D = 180 ( angles on st line)

110+D =180

D=70

D=F ( opposite angles of parallelogram are congurent)

so F=70

3 0

3 years ago

What is the quotient and remainder for 52 ÷ 8

Andrej [43]

the quotient is 6 and the reamainder is 4

7 0

3 years ago

Someone please go through this with me I beg, I will award brainiest! Maths homework due in for the 8th.. ;((

enot [183]

Essentially, you're going to want to reverse the steps on x in order to isolate it from the rest of the variables. To do this, perform inverse operations on x. The first one of these is the multiplication of x and m, so divide both sides by m to cancel m out on the right side. Now we have y/m = x + b. The final thing to do in order to isolate x is to subtract b from both sides. This yields us y/m - b = x. This can be rearranged into x = y/m - b, which should be your answer.

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3 years ago