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Zanzabum
3 years ago
8

a parabola has x intercepts of -1 and 3 it passes through the point (1,6) write the equation if the parabola

Mathematics
1 answer:
matrenka [14]3 years ago
3 0

\boxed{f(x)=-\frac{3}{2}x^2+3x+\frac{9}{2}}

<h2>Explanation:</h2>

The Standard Form of the equation of a parabola is given by the form:

y=ax^2+bx+c

As y is a function of x, then we can write:

y=f(x)=ax^2+bx+c \\ \\ a, \ b, c \ Real \ Coefficients

Also, we can write f(x) in factored form as:

f(x)=a(x-x_{1})(x-(x_{2}) \\ \\ x_{1} \ and \ x_{2} \ Are \ the \ roots

In this case:

x_{1}=-1 \\ \\ x_{2}=3

So:

f(x)=a(x-(-1))(x-3) \\ \\ f(x)=a(x+1)(x-3)

We also know that the parabola passes through the point (1,6):

f(1)=6=a(1+1)(1-3) \\ \\ Isolating \ a: \\ \\ 6=a(2)(-2) \\ \\ 6=a(-4) \\ \\ a=-\frac{6}{4} \\ \\ a=-\frac{3}{2}

Finally, the equation of the parabola is:

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

Or applying Distributive Property:

f(x)=-\frac{3}{2}\left(x^2-2x-3\right) \\ \\ \boxed{f(x)=-\frac{3}{2}x^2+3x+\frac{9}{2}}

<h2>Learn more:</h2>

Piecewise-defined function: brainly.com/question/12169258

#LearnWithBrainly

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Given sinθ=4/7 and θ lies in Quadrant II .
AlladinOne [14]

Answer:−√33/7


Step-by-step explanation:

Second quadrant implies cos negative, as cos is projection from

unit circle to x axis.

sin^2+cos^2=1

cos= sqrt(1-sin^2)

sin^2 = 16/49

1-sin^2 = 33/49

sin= -sqrt(33)/7

5 0
3 years ago
D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x
MA_775_DIABLO [31]
The solution depends on the value of k. To make things simple, assume k>0. The homogeneous part of the equation is

\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0

and has characteristic equation

r^2-16k=0\implies r=\pm4\sqrt k

which admits the characteristic solution y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}.

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be y_p=ae^{4x}+be^x. Then

\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x

So you have

16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x
(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x

This means

16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}
b(1-16k)=30\implies b=\dfrac{30}{1-16k}

and so the general solution would be

y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x
8 0
3 years ago
Brainliest!
ololo11 [35]

Answer:

  • y ≥ x² -2x -3
  • y ≤ x +3

Step-by-step explanation:

When matching graph to inequality, the first things to look for are the nature of the boundary line (solid or dashed), and the direction of shading relative to the boundary line (above or below, left or right).

<h3>Boundary line</h3>

The boundary line of the solution set of an inequality will be solid if the line is <em>included</em> in the solution. That is, the inequality will include the "or equal to" case. The corresponding inequality symbols are ≤ or ≥.

The boundary line of the solution set will be dashed if the line is <em>not included </em>in the solution. The corresponding inequality symbols are < or >.

<h3>Shading</h3>

The shading will be above the boundary line if the solution set includes larger y-values than those on the boundary. This will be the case when the inequality is of the form y > ( ) or y ≥ ( ).

For inequalities of the form y < ( ) or y ≤ ( ), the shading will be below the boundary line.

Similarly, the shading for an inequality of the form x > ( ) will be right of the boundary line, where x-values are greater. For inequalities of the form x < ( ), the shading will be to the left of the boundary line.

<h3>Application</h3>

In the given graph, both boundary lines are solid, so both inequalities will include the "or equal to" case. This eliminates choices A, B, D.

The shading is above the quadratic boundary line, and below the linear boundary line, so the inequalities can be expected to be of the forms ...

  • y ≥ x² +...
  • y ≤ x +...

These forms match choice C:

  • y ≥ x² -2x -3
  • y ≤ x +3
7 0
2 years ago
What is 0.118 in expanded form
antoniya [11.8K]

Answer:

zero and one-hundred eighteen-thousandths

4 0
4 years ago
What is the equation of a line with a slope of -8 and an ordered pair (4,-3)?
lisabon 2012 [21]
You can solve this easily using point slope form: y-y1 = m(x-x1)
Substitute the given y value in for y1 and the given x for x1, and substitute the slope in for m.
To put it in slope intercept form, isolate y.
Hope this helps!
6 0
3 years ago
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