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tensa zangetsu [6.8K]
3 years ago
7

Use the parabola tool to graph the quadratic function. f(x)=2x2+12x+16

Mathematics
2 answers:
shepuryov [24]3 years ago
8 0

Answer:

Step-by-step explanation:

To obtain the graph of a parabola, three data are necessary: ​​the vertex (the vertex is the highest or lowest point of the graph corresponding to the parabola and there it is on the plane of symmetry of the parabola), the roots ( those values ​​of x for which the expression is 0. Graphically,  the roots correspond to the abscissa of the points where the parabola  cuts the x-axis.) and the concavity.

Being f(x)=ax²+bx+c, you can see that, in this case, a=2, b=12 and c=16. So:

  • Vertex= for your calculation, xv=\frac{-b}{2*a}=\frac{-12}{2*2}, so xv=-3. Now that you know x, all you have to do is enter its numerical value into the original formula to find yv. yv=2*(-3)²+12*(-3)+16. Then yv=-2
  • Roots:  The roots are calculated using the expression: x1,x2=\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}. Replacing the values that you have:x1,x2=\frac{-12+-\sqrt{12^{2}-4*2*16 } }{2*2} Solving, you obtain x1=-2 and x2=-4
  • Concavity: If a> 0 (positive) the parabola is concave or pointed upwards, while if a <0 (negative) the parabola is convex or pointed downwards. In this case a = 2, so the parabola opens upward, being concave.

In this way, the graph shown in the attached image is obtained.

yKpoI14uk [10]3 years ago
7 0
We have that
<span>f(x)=2x</span>²<span>+12x+16

using a graph tool
see the attached figure</span>

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HELP PLEASE I DONT UNDERSTAND
miv72 [106K]

Answer:

None of these

Step-by-step explanation:

A <u>perpendicular bisector</u> is a segment which intersects a given segment at a 90° angle, and passes through the given segment's midpoint. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a perpendicular bisector.

A <u>median</u> of the triangle is a segment joining a vertex to the midpoint of the opposite side. Since point T divides segment SU into two parts with lengths 46 and 62 units, VT is not a median.

An <u>altitude</u> of the triangle is a segment passing through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). The diagram doesn't show the right angle at point T (VT is not perpendicular to SU), then VT is not an altitude.

Thus, option None of These is true.

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2 years ago
Five more than a number p is less than 17.
saw5 [17]

Answer:

p+5 <17

Step-by-step explanation:

3 0
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Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give
frutty [35]

Answer:

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this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

g(x) =e^{x^3}

  • we know that \frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)

g'(x) =e^{x^{3}}(3 x^{2})

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this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}

using the equation of line:

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we'll find the equation of the tangent line.

here (x1,y1) =(-1,1/e), and m = 3/e

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y=\dfrac{3x}{e}+\dfrac{4}{e}

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