Needing some help, please ?(: & Thank you ♥

For questions 3–4, order the group of quadratic functions from widest to narrowest graph.

y = 3x2, y = x2, y = 2x2

y = 2x2, y = x2, y = 3x2

y = 3x2, y = 2x2, y = x2

y = x2, y = 2x2, y = 3x2

y = x2, y = 3x2, y = 2x2

y = –5x2, y = –x2, y = –4x2

y = –x2, y = –5x2, y = –4x2

y = –x2, y = –4x2, y = –5x2

y = –5x2, y = –4x2, y = –x2

y = –4x2, y = –x2, y = –5x2

How is the graph of y = 4x2 + 1 different from the graph of y = 4x2?

It is shifted 1 unit up.

It is shifted 1 unit down.

It is shifted 1 unit left.

It

Question

pandasim0ari2aLi pandasim0ari2aLi

06-12-2016
Mathematics

Answered

Needing some help, please ?(: & Thank you ♥

For questions 3–4, order the group of quadratic functions from widest to narrowest graph.

y = 3x2, y = x2, y = 2x2

y = 2x2, y = x2, y = 3x2

y = 3x2, y = 2x2, y = x2

y = x2, y = 2x2, y = 3x2

y = x2, y = 3x2, y = 2x2

y = –5x2, y = –x2, y = –4x2

y = –x2, y = –5x2, y = –4x2

y = –x2, y = –4x2, y = –5x2

y = –5x2, y = –4x2, y = –x2

y = –4x2, y = –x2, y = –5x2

How is the graph of y = 4x2 + 1 different from the graph of y = 4x2?

It is shifted 1 unit up.

It is shifted 1 unit down.

It is shifted 1 unit left.

It

Verified Answer :

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parmesanchilliwack parmesanchilliwack · Answer 1 · 2019-01-07T07:20:09-05:00

Answer:

3)\(y = x^2\), \(y = 2x^2\), \(y = 3x^2\)

4) \(y = -x^2\),\(y = -5x^2\), \(y = -4x^2\)

5) It is shifted 1 unit up.

Step-by-step explanation:

3) Since, the general equation of parabola is,

\(f(x) = a(x-h)^2+k\)

If 0<a<1 then f(x) is wider than \(f(x)=x^2\)

If a>1 then f(x) is narrow that \(f(x)=x^2\)

Thus, the required sequence of equations from widest to narrow graph,

\(y = x^2\), \(y = 2x^2\), \(y = 3x^2\)

4) Again if a<0 then \(f(x)=-a(x-h)^2+k\) is wider than \(f(x)= -x^2\)

Thus, the required sequence from widest to narrowest graph is,

\(y = -x^2\),\(y = -5x^2\), \(y = -4x^2\)

5) Since, In equation of parabola,

\(f(x) = a(x-h)^2+k\)

k shows the y-coordinate of the vertex of the parabola,

⇒ k shows the shifting along y-axis.

Thus, If the graph \(y=4x^2\) is transformed to \(y=4x^2+1\)

Then we will say it is shifted 1 unit up or shifted vertically by the factor 1.

Therefore, First Option is correct.

AkhileshT AkhileshT · Answer 2 · 2019-09-06T03:03:33-04:00

Question (3): The correct option is \(\boxed{\bf option (d)}\).

Question (4): The correct option is \(\boxed{\bf option (c)}\).

Question (5): The correct option is \(\boxed{\bf option (a)}\).

Further explanation:

Question (3):

Solution:

The best method to find which graph is widest and narrowest is graphing a quadratic function.

The vertically stretching of graph of \(f(x)\) by a factor of \(c\) can be obtained by \(g(x)=cf(x)\) if \(c\) is greater than \(1\).

The graph is stretched as we increase the value of \(c\) in first case the value of \(c\) is \(1\) and in the second case the value of \(c\) is \(2\) and the third case is value of \(c\) is \(3\).

It means that the third case has maximum stretching that leads to a narrow graph, and similarly in second case the value of \(c\) is \(2\) it is also stretches but less than the third case.

Therefore, the order of quadratic functions from widest to narrowest graph is as follows:

\(\boxed{(y=x^{2})>(y=2x^{2})>(y=3x^{2})}\)

Figure 1 (attached in the end) represents the graph of the functions \(y=x^{2},y=2x^{2},y=3x^{2}\).

Thus, the correct option is \(\boxed{\bf option (d)}\).

Question (4):

Solution:

The reflection of graph of \(f(x)\) about \(x\)-axis can be obtained by \(g(x)=-f(x)\).

The graph of the function \(y=-x^{2}\) is obtained when each point on the curve of the function \(y=x^{2}\) is reflected across the \(x\)-axis.

Similarly, the graph of the function \(y=-4x^{2}\) \(y=-5x^{2}\) and is obtained when each point on the curve of the function \(y=4x^{2}\) and \(y=5x^{2}\) is reflected across the \(x\)-axis respectively.

From figure 2 (attached in the end) it is observed that the graph of the function \(y=-x^{2}\) is the widest and the graph of the function \(y=-5x^{2}\) is the narrowest.

Therefore, the correct option is \(\boxed{\bf option (c)}\).

Question (5):

Solution:

If a constant is added to a function, the graph of the function shifts vertically upwards if the constant is positive and it shifts vertically downwards if the constant is negative.

For example: The graph of the function of the form \(y=f(x)+a\) is obtained when each point on the curve of \(y=f(x)\) is shifted along the \(y\)-axis. If \(a\) is positive then the curve shifts vertically upwards and if \(a\) is negative then the curve shifts vertically downwards.

Similarly, the graph of the function \(y=4x^{2}+1\) is obtained when each point on the curve of \(y=4x^{2}\) shifts \(1\text{ unit}\) vertically upwards.

Figure 3 (attached in the end) represents the graph of the function \(y=4x^{2}\) and \(y=4x^{2}+1\).

Therefore, the correct option is \(\boxed{\bf option (a)}\).

Learn more:

1. Representation of graph https://brainly.com/question/2491745

2. Quadratic equation: https://brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Topic: Shifting of graph

Keywords: Graph,inequality ,y=x^2 ,y=-4x^2 ,y=-5x^2 ,y=x^2 ,y=2x^2 , y=3x^2, shifted, stretches, widest, narrowest, quadratic function shifting, translation, curve.