Solve the inequality/ 3p

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

Directions: Match the product and quotients estimates below with the correct expression on the left

prohojiy [21]

Answer:

Answer is in attached image.

Step-by-step explanation:

Given the expressions, for which we have to find the estimates as per the expressions on the left.

The given expressions are:

1) 35 $\times$ 23

2) 132 $\div$ 168

3) 17.3 $\times$ 18.4

4) 999 $\div$ 208

5) 998 $\times$ 211

Here, we need to find the rounded off numbers.

35 can be rounded to 40 and 23 to 20.

Therefore, equivalent to 35 $\times$ 23 is 40 $\times$ 20

132 can be rounded to 130 and 168 to 170.

Therefore, equivalent to 132 $\div$ 168 is 130 $\div$ 170.

17.3 can be rounded to 17.0 and 18.4 to 18.0.

Therefore, equivalent to 17.3 $\times$ 18.4 is 17.0 $\times$ 18.0.

999 can be rounded to 1000 and 208 to 210.

Therefore, equivalent to 999 $\div$ 208 is 1000 $\div$ 210.

998 can be rounded to 1000 and 211 to 210.

Therefore, equivalent to 998 $\times$ 211 is 1000 $\times$ 210.

The solution can be found in the attached image as well.

8 0

2 years ago

If b=33.2 and B=61° find a (picture provided)

kow [346]

For this case we have to, by definition:

$tg (B) = \frac {33.2} {a}$

This means that the tangent of angle B will be equal to the leg opposite the angle on the leg adjacent to the same angle.

Then, clearing to have:

$a = \frac {33.2} {tg (61)}\\a = \frac {33.2} {1.80404776}\\a = 18.403060$

Rounding out the value of a we have:

$h = 18.4$

Answer:

Option C

6 0

3 years ago

Read 2 more answers

Find the smallest number such that the remainder is 3 when it is divided by 16,20 or 24.

schepotkina [342]

Answer: 123

Step-by-step explanation:

Foe us to solve this, we have to find the lowest common multiple of 16, 20 and 24 first and then add 3 to the LCM. This goes thus:

Multiples of 16 = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160

Multiples of 20 = 20, 40, 60, 80, 10, 120, 140, 160

Multiples of 24 = 24, 48, 72, 96, 120

Therefore, the Lowe's common multiple is 120.

We then add the remainder of 3 and this will give:

= 120 + 3

= 123

4 0

2 years ago

3 times the measure of an angle is 14 less than the measure of its complement. What is the measure of the angle? A.19° B. 57° C.

kodGreya [7K]

A. is the answer. I just took the test

4 0

3 years ago

Solve the inequality/ 3p - 2.5 < 6.5