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Natasha2012 [34]
2 years ago
8

explain the benefits of each of the three forms of quadratic equations, standard form, vertex form, and factored form. What do t

hey reveal about the graph or the quadratic?
Mathematics
1 answer:
mamaluj [8]2 years ago
4 0

Answer:

Summary:

Standard form allow us to quickly find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Step-by-step explanation:

The three forms of quadratics are the standard form, vertex form, and the factored form. Each of them reveals a specific part about the quadratic.

Standard Form:

The standard form of a quadratic is:

ax^2+bx+c

There are only two details that can be conveyed by a quadratic in standard form immediately: (1) the leading coefficient a, and (2) the y-intercept.

The leading coefficient a will tell us if the parabola curves upwards or downwards.

And the constant c will give us the y-intercept.

Vertex Form:

The vertex form of a quadratic is:

a(x-h)^2+k

There are also two details that can be conveyed by a quadratic in vertex form:  (1) the vertex, and (2) the leading coefficient.

The leading coefficient is given by a. Again, this tells us the orientation of the parabola.

And the vertex is given by (h, k).

Hence, in my opinion, vertex form is the best form of a quadratic since it immediately reveals the vertex, the most important aspect of a quadratic.

Factored Form:

The factored form of a quadratic is:

a(x-p)(x-q)

Where p and q are the zeros/roots/solutions of the quadratic.

Again, factored form gives us two details about the quadratic: (1) the leading coefficient, and (2) the zeros.

The zeros tells us when the parabola crosses the x-axis, which can assist in graphing.

Summary:

Therefore, each form of a quadratic equation has its own benefits.

Standard form allow us to find the y-intercept.

Vertex form allow us to quickly locate the vertex.

And factored form allows us to quickly determine the roots/zeros.

Hence, depending on the question, each form can be useful in its own way.

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Allisa [31]

Since the discriminant given has a value that is greater than zero, hence  the roots of the quadratic equation are real and distinct.

<h3>Discriminant of a quadratic equation</h3>

Quadratic equation is an equation that has a leading degree of 2. The discriminant is used to determine the nature of the equation

If D > 0 , the roots of the quadratic equation are real and distinct.

If D < 0 , the roots of the quadratic equation are complex

Since the discriminant given has a value that is greater than zero, hence  the roots of the quadratic equation are real and distinct.

Learn more on discriminant here: brainly.com/question/2507588

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1 year ago
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2, use the given sample sizes and numb
11Alexandr11 [23.1K]
Since the data is insufficient. Let us denote that n1 = 100, n2 = 100X1 = 38. X2 = 40
So looking for the p value:
p = (38+ 40) / (100 + 100) = 0.39
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3 years ago
Juan told Sylvia he got a $0.50 raise this week and his new hourly rate will be $10.25 an hour. Sylvia wants to know what Juan’s
zhenek [66]

Answer:

The correct answer is:

r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.

This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).

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- 4 w - 4 = - 24
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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

<u>Step 1:</u> 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

<u>Step 2:</u> Substituting values for the variables

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

<u>Step 3:</u> Simplifying the right side

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

<u>Step 4:</u> Multiplying by the reciprocal

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

<u>Therefore, Base Area of the Cone=15 Square Inches</u>

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3 years ago
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