# Graphing Quadratic Functions

The quadratic function is
the polynomial function with the highest variable power is 2.

The general form of
quadratic function equations is:

f(x) = ax

^{2}+ bx + x or
y = ax

^{2}+ bx + c; a ≠ 0
a function is always related to the function graph. Likewise with the quadratic function where the graph of the quadratic function is called a satellite dish. To illustrate the graph of the quadratic function, it must be determined at the intersection with the axis of the coordinate and the extreme point (peak point / maximum point. / Minimum point). Where the complete step is

Steps Describe the Graph of Quadratic Functions y = ax

^{2}+ bx + c
1. Determine the direction of the parabolic chart up or down by looking at the value of a

- If the value of a> 0 then the satellite dish opens up and has a minimum extreme value.
- If the value of a <0 then the satellite dish opens down and has a maximum extreme value.

2. Determine the intersection
with the coordinate axis.

The intersection of the x axis if y = 0. So

The
values of x

_{1}and x_{2}will be known to use factoring, if it is difficult to get the previous results, check the value first.- If D < 0, then the function does not have the roots of quadratic equations so the graph sketch of the quadratic function does not cut the X-axis.
- If D> 0, then the function has the roots of the quadratic function equation but we have difficulty solving the solution because the number that is factored is a decimal number. Where the values of these roots can be obtained by the
**abc formula**, After we get the values x_{1}and x_{2}, the intersection points of the quadratic function are (x_{1}, 0) and (x_{2}, 0)

- The intersection with the Y axis if x = 0 because x = 0 then y = c and the intersection point is (0, c).

4. Determine the position of the graph of the square function of the X axis.

- If D > 0 then the graph of the quadratic function intersects the X-axis at two points.
- If D = 0, then the graph of the quadratic function alludes to the X-axis at one point
- If D <0 then the graph of the quadratic function does not cut the X-axis.

**Example 1.**

Find the deskriminan value, the intersection point, the extreme point of the quadratic equation of f(x) = x

^{2}- 6x + 5?
Answer:

**The intersection of the X-axis**is obtained if y = 0, then the form of the quadratic equation becomes

x

^{2}- 6x + 5 = 0
To ensure that the quadratic equation above has a square root, we must look for the discriminant value.

D = b

^{2}– 4ac = (-6) – 4(1)(5) = 36 – 20 = 16
Because the discriminant value is 16 (positive / more than 0) the quadratic equation must have two (square roots) different real and two intersections of the x axis. The intersection of the X axis is obtained from the roots of the quadratic equation,

x

^{2}– 6x + 5 = 0
(x – 1)(x – 5)

x = 1 or x = 5

So, the intersection of the x-axis is (1, 0) and (5, 0).

**The intersection of the Y-axis**

The intersection with the Y-axis is obtained if the value of x = 0.

y = x

^{2}– 6x + 5
y = (0)

^{2}– 6 (0) + 5 = 5
So, the intersection of the Y axis is (0, 5).

**The Extreme Point**

The extreme point of the quadratic function f(x) = y = ax

^{2}+ bx + c is
The symmetrical axis is x = 3 and the extreme value is - 4.

After obtaining the
intersection of the X axis, the intersection of the Y axis, the extreme point,
we can draw a graph of the quadratic function. Where the quadratic f(x) = x

^{2}- 6x + 5 has a intersection of the X axis: and (5, 0), the intersection of the Y axis: (0, 5) and extreme points (3, -4). Draw the points on the Cartesian coordinates as shown below,
Then connect the points with a smooth curve, so that the quadratic function curve f(x) = x

^{2}- 6x + 5 will be obtained as follows,**Example 2.**

If the function f(x) = qx

^{2}– (q+2)x – 6 reaches the highest value for x = -1, specify the value of q?
Answer:

x = -1 is a symmetrical
axis, then

**Example 3.**

Find the extreme point and
intersection of the X axis for the square function f(x) = x

^{2}– 20x + 75.
Answer:

If the intersection of X
with the condition y = 0, the extreme point for the quardat function y = x

^{2}– 20x + 75 is
The intersection of the X-axis

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