188k views
2 votes
Sketch the graph for the following quadratic function.


- x ^(2) + 4x + 12
it's ok if it's wrong.i just wanna see how the work done to do this

1 Answer

3 votes

Answer:

Please refer to the attached image for the graph of given function.

Explanation:

Given the equation:


-x^(2) +4x+12

Let us rewrite by letting it equal to
y.


y=-x^(2) +4x+12

Now, we can see that it is a quadratic equation and it is known that a quadratic equation has a graph of parabola.

Let us compare the given equation with standard quadratic equation:


y=ax^(2) +bx+c

we get:


a = -1\\b = 4\\c = 12

Coefficient of
x^(2) is negative 1, so the parabola will open downwards.

Axis of symmetry: It is the line which will divide the parabola in two equal congruent halves.

Formula for axis of symmetry is:


x = -(b)/(2a)


x = -(4)/(2(-1))\\\Rightarrow x=2

It is shown as dotted line in the image attached in the answer area.

Axis of symmetry will also contain the vertex of the parabola.

It is a downward parabola so vertex will be the highest point on this parabola.

Putting x = 2 in the equation of parabola:


y=-2^(2) +4* 2+12\\\Rightarrow y =16

So, vertex will be at P(2, 16).

Now, let us find points of parabola to sketch graph:

put x = 0,
y=-0^(2) +4* 0+12=12

Another point is Y(0,12)

Now, let us put y = 0, it will give us two points because the equation is quadratic in x.


0=-x^(2) +4x+12\\\Rightarrow -x^(2) +6x-2x+12=0\\\Rightarrow -x(x -6)-2(x-6)=0\\\Rightarrow (-x-2)(x-6)=0\\\Rightarrow x = -2, 6

So, other two points are X1(-2, 0) and X2(6,0).

If we plot the points P, Y, X1 and X2 we get a graph as attached in the image in answer area.

Sketch the graph for the following quadratic function. - x ^(2) + 4x + 12​ it's ok-example-1
User Thebitguru
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories