Graphing points for y=|2x-1| Pls help first person to answer get the Brainly points

I have these factoring questions I need help with.

snow_lady [41]

$f(x)=4x^2+4x-3$

1. Determine y-intercept.

The y-intercept is (0,-3). Substitute x = 0 in the equation as we get f(x) = -3 as the y-intercept.

2. Determine the zeros.

Factor the polynomials first. $(2x-1)(2x+3)$ This is the factored form. The zeros are the roots of equation. Therefore, the zeros are 1/2 and -3/2

3. Determine the Axis of Symmetry

We can solve this by using the formula of $x=-\frac{b}{2a}$ However, I'll be solving the Axis of Symmetry with Calculus instead.

$f'(x)=2(4x^{2-1})+1(4x^{1-1})-0\\f'(x)=8x+4$

Then let f'(x) = 0 to find the Axis of Symmetry.

$8x+4=0\\8x=-4\\x=-\frac{4}{8}\\x=-\frac{1}{2}$

Therefore, the Axis of Symmetry is -1/2

4. Determine the vertex.

Substitute the value of Axis of Symmetry in f(x).

$f(x)=4(-\frac{1}{2})^2+4(-\frac{1}{2})-3\\f(x)=4(\frac{1}{4})-2-3\\f(x)=1-2-3\\f(x)=-4$

Therefore the vertex is at (-1/2, -4)

5. Does the vertex representing max-pont or min-point?

The vertex represents the minimum point. The graph is upward, meaning the minimum point is the point that gives the LOWEST Y-VALUE.

7. Graph f(x)

Unfortunately I won't be able to graph. But I can tell you to graph a parabola that has the most curve at the vertex and intercepts y-axis at (0,-3).

--------------------------- End of Part 1 --------------------------------

2. Write the general form of Quadratic Function in standard form.

$y=ax^2+bx+c$

The graph can be easily determined about the y-intercept and being an upward or downward parabola along with how narrow or wide the parabola is.

For example, c value is the y-intercept as defined. When a > 0, the parabola is upward and when a < 0, the parabola is downward. The more value of | a | is, the more narrow it will be and the less value of | a | it is, the wider it will be.

3. Write in Factored Form

$y=(x+a)(x+b)\\y=(x-a)(x-b)\\y=(x+a)(x-b)\\y=(x-a)(x+b)$

These are factored forms with different types of operators.

The equation can be easily determined about the roots of equation. For example, if the function is in f(x) = (x+2)(x-1) Then the roots would be x = -2 and 1 as the graph will intercept x-axis at (-2,0) and (1,0)

4. Write in Vertex Form.

$y=a(x-h)^2+k$

The equation can be easily determined for the vertex, axis of symmetry and the same narrow/wide/upward/downward parabola again.

The vertex is at (h,k) and the axis of symmetry is at x = h.

For example, $y=(x-2)^2+3$

The vertex would be at (2,3) and the axis of symmetry is x = 2.

3 0

3 years ago

Select from the drop-down menu to correctly compare the numbers.

OverLord2011 [107]

This questions can be answered with a calculator, but I have an impression it is meant to be a mental calculation problem, which can be solved as follows.

We know that 10*10=100, in otherwords, √ 100 = 10 which is greater than 9.4247.

We also know that √ 108 is greater than √ 100 =10

So we can conclude that
√ 108 > √ 100 = 10 > 9.4247
or simply

√ 108 > 9.4247

by the transitive property of logical propositions.

6 0

3 years ago

Which problem could be solved with the expression 4 × (6+3)?

rodikova [14]

Answer:

C. Mason goes on vacation with her family for 4 days. Each morning, she bikes 6 kilometers to the donut shop and then 3 more kilometers to the swimming hole. She rides home from the swimming hole in her mom's car. How many kilometers does Mason bike on vacation?

Step-by-step explanation:

For A., the equation would be 4 + 6 - 3

For B., the equation would be 3 x (6 + 4)

So our only option is C.

For C., the equation would be 4 x (6 + 3)

8 0

3 years ago

Read 2 more answers

Which equation illustrates the division property of equality? PLEASE HELP ME!!

Mekhanik [1.2K]

C does. 8f = 40 divide both sides by 8 to get f=5

8 0

2 years ago

A group of health care workers were asked how many times per week they visited a gym. The data is shown on the dot plot. Select

fiasKO [112]

Answer:

the answer is b i think

Step-by-step explanation:

6 0

2 years ago