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How to do graphs of quadratic functions

Anastaziya [24]

Answer:

The Graph of a Quadratic Function

A quadratic function is a polynomial function of degree 2 which can be written in the general form.

Step-by-step explanation:

Example: Graph: f(x)=−x2−2x+3.

Solution:

Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).

f(x)f(0)===−x2−2x+3−(0)2−2(0)+33

The y-intercept is (0,3).

Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.

f(x)000x+3x======−x2−2x+3−x2−2x+3x2+2x−3(x+3)(x−1)0−3orx−1x==Set f(x)=0.Multiply both sides by −1.Factor.Set each factor equal to zero.01

Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).

Step 3: Determine the vertex. One way to do this is to first use x=−b2a to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.

x====−b2a−(−2)2(−1)2−2−1

Substitute −1 into the original function to find the corresponding y-value.

f(x)f(−1)====−x2−2x+3−(−1)2−2(−1)+3−1+2+34

The vertex is (−1,4).

Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.

x −2 y 3f(−2)=−(−2)2−2(−2)+3=−4+4+3=3Point(−2,3)

Our fifth point is (−2,3).

Step 5: Plot the points and sketch the graph. To recap, the points that we have found are

y−intercept:x−intercepts:Vertex:Extra point:(0,3)(−3,0) and (1,0)(−1,4)(−2,3)

Answer:

4 0

3 years ago

One-eighth of a number is -4,200. What is the number?

joja [24]

-33,600. To get this you multiply -4,200 by 8

4 0

3 years ago

Applying the Procedure

Verizon [17]

Answer:

15 Square Inches

Step-by-step explanation:

Volume of the cone=40 cubic inches

Height of the cone=8 Inches

Step 1: Applying the formula for the volume of a cone

Volume of a Cone $=\frac{1}{3}\pi r^2 h=\frac{1}{3} X $Base Area X Height$

Step 2: Substituting values for the variables

$40=\frac{1}{3} X $Base Area X 8$

Step 3: Simplifying the right side

$40=\frac{8}{3} X $Base Area$

Step 4: Multiplying by the reciprocal

$40X\frac{3}{8}=\frac{8}{3} X\frac{3}{8} X $Base Area\\$

Therefore, Base Area of the Cone=15 Square Inches

8 0

3 years ago

1.The base length of a rectangle is multiplied by 8. How does this affect the area?

stiv31 [10]

Answer:

1. C - 8x bigger

2. D - 16x bigger

3. A - 3x bigger

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Which of the following is NOT a rational number?

makvit [3.9K]

Answer:

A rational number is a number that can be expressed as a fraction (the ratio of two integers).

Integer: A whole number that can be positive, negative, or zero.

To calculate if each radical can be expressed as a rational number, convert the decimals into rational numbers, then simplify:

$\sqrt{121}=\sqrt{11^2}=11=\dfrac{11}{1} \quad \leftarrow \textsf{rational}$

$\sqrt{12.1}=\sqrt{\dfrac{1210}{100}}=\dfrac{\sqrt{1210}}{\sqrt{100}}=\dfrac{\sqrt{121\cdot 10}}{10}=\dfrac{\sqrt{121}\sqrt{10}}{10}=\dfrac{11\sqrt{10}}{10} \leftarrow \textsf{not rational}$

$\sqrt{1.21}=\sqrt{\dfrac{121}{100}}=\dfrac{\sqrt{121}}{\sqrt{100}}=\dfrac{\sqrt{11^2}}{\sqrt{10^2}}=\dfrac{11}{10} \leftarrow \textsf{rational}$

$\sqrt{0.0121}=\sqrt{\dfrac{121}{10000}}=\dfrac{\sqrt{121}}{\sqrt{10000}}=\dfrac{\sqrt{11^2}}{\sqrt{100^2}}=\dfrac{11}{100} \leftarrow \textsf{rational}$

Therefore, $\sf \sqrt{12.1}$ is not a rational number.

5 0

2 years ago