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Nikitich [7]
3 years ago
13

(5 pts) A quadratic function f is given by f(x) = ax2 + bx + c where a is not 0. Select all

Mathematics
1 answer:
Vsevolod [243]3 years ago
8 0

Answers:

  • a) True. Plug in x = 0 and it leads to y = c. Therefore, the point (0,c) is on the parabola.
  • b) False. Plug in y = 0 and apply the quadratic formula. One x intercept may sometimes be x = c, but it could easily be other values as well. Or perhaps you may not get any real number solutions at all. See part d) below.
  • c) True. If a < 0, then the leading coefficient is negative. Overall, both endpoints will tend toward negative infinity to produce a parabola that opens downward.
  • d) False. The quadratic may have one x intercept or it may not have any x intercepts at all. It depends on what the discriminant d = b^2 - 4ac is equal to. If d < 0, then we have no x intercepts. If d = 0, then we have exactly 1 x intercept. If d > 0, then we have two different x intercepts.
  • e) True. The vertex's x coordinate is -b/(2a). If b = 0, then the x coordinate of the vertex is 0. The vertical line x = 0 is directly on top of the y axis.
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Is 11/20 greater than a half
Rainbow [258]
Yes... a half is equal to 10/20 and 11/20 is greater than 10/20 so 11/20 is greater than a half
8 0
2 years ago
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If f(x)=2x^3-6x^2-16x-20f(x)=2x *3 −6x *2−16x−20 and f(5)=0, then find all of the zeros of f(x)f(x) algebraically.
mihalych1998 [28]

The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

<h3>How to obtain the solutions to the equation?</h3>

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 =  = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

  • a = 2.
  • -5c = -20 -> c = 4.
  • b = -6 + 5a = 4.

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

  • x = -1 + i.
  • x = -1 - i.

More can be learned about the solutions of an equation at brainly.com/question/25896797

#SPJ1

8 0
10 months ago
Select the correct answer.
Pie

Answer:

a.

Step-by-step explanation:

a= y-k/ (x-h)^2

<h2>Make me a brain list</h2>
6 0
1 year ago
Solve this problem please <br> x/3+6-2x=-6
Nikolay [14]

Answer:

36/5

Step-by-step explanation:

x/3 + 6 -2x = -6

multiply the whole equation by 3 to get rid of the denominator of the first x term.

x+18-6x = -18

move x terms to one side and numerical terms to the other, subtract 18 from both sides in this case

x+18-6x-18=-18-18

x-6x = -36

simplify

-5x = -36

divide both sides by -5 to isolate x

x = -36/-5

=36/5

3 0
3 years ago
What is the product? (9 t minus 4)(negative 9 t minus 4) negative 81 t squared minus 16 negative 81 t squared + 16 negative 81 t
liraira [26]

The product is negative 81 t squared + 16 ⇒ 2nd answer

Step-by-step explanation:

The product of two binomials (ax + b)(cx + d), where a, b, c, and d are constant

  • Multiply (ax) by (cx) ⇒ 1st × 1st
  • Multiply (ax) by (d) and (b) by (cx) ⇒ ext-reams and nears
  • Add the two products ⇒ like terms
  • Multiply (b) by (d) ⇒ 2nd × 2nd

Let us find the product of (9 t - 4) and (-9 t - 4)

Multiply the 1st two terms

∵ (9 t)(-9 t) = -81 t²

Multiply the ext-reams

∵ (9 t)(-4) = -36 t

Multiply the nears

∵ (-4)(-9 t) = 36 t

Add the like terms

∵ -36 t + 36 t = 0

Multiply the 2nd two terms

∵ (-4)(-4) = 16

Write the answer

∴ (9 t - 4)(-9 t - 4) = -81 t² + 0 + 16

∴ (9 t - 4)(-9 t - 4) = -81 t² + 16

The product is  -81 t² + 16

Learn more:

You can learn more about the product of algebraic expressions in brainly.com/question/1617787

#LearnwithBrainly

7 0
3 years ago
Read 2 more answers
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