5 2 On A Graph

About Graphing Quadratic Functions

Quadratic function has the form $ f(ten) = ax^2 + bx + c $ where a, b and c are numbers

You can sketch quadratic role in four steps. I volition explain these steps in following examples.

Instance i:

Sketch the graph of the quadratic role

$$ {\colour{blueish}{ f(x) = x^2+2x-three }} $$

Solution:

In this example nosotros have $ a=1, b=ii $ and $c=-three$

STEP one: Find the vertex.

To find x - coordinate of the vertex we use formula:

$$ ten=-\frac{b}{2a} $$

So, we substitute $1$ in for $a$ and $2$ in for $b$ to become

$$ x=-\frac{b}{2a} = -\frac{ii}{2\cdot1} = -ane $$

To find y - coordinate plug in $x=-one$ into the original equation:

$$ y = f(-1) = (-1)^2 + 2\cdot(-1) - iii = one - 2 - 3 = -four $$

And then, the vertex of the parabola is $ {\colour{red}{ (-ane,-4) }} $

Stride two: Find the y-intercept.

To find y - intercept plug in $ten=0$ into the original equation:

$$ f(0) = (0)^2 + 2\cdot(0) - iii = 0 - 0 - 3 = -3 $$

So, the y-intercept of the parabola is $ {\colour{bluish}{ y = -3 }} $

STEP 3: Detect the x-intercept.

To discover 10 - intercept solve quadratic equation $f(x)=0$ in our case we accept:

$$ x^2+2x-3 = 0 $$

Solutions for this equation are:

$$ {\color{bluish}{ x_1 = -iii }} ~~~\text{and}~~~ {\colour{blue}{ x_2 = i }} $$

( to learn how to solve quadratic equation employ quadratic equation solver )

STEP 4: plot the parabola.

Example 2:

Sketch the graph of the quadratic function

$$ {\color{blue}{ f(x) = -ten^2+2x-2 }} $$

Solution:

Here nosotros have $ a=-one, b=ii $ and $c=-2$

The x-coordinate of the vertex is:

$$ {\color{bluish}{ x = -\frac{b}{2a} }} = -\frac{2}{two\cdot(-1)}= 1 $$

The y-coordinate of the vertex is:

$$ y = f(i) = -1^ii+2\cdot1-2 = -1 + ii - two = -1 $$

The y-intercept is:

$$ y = f(0) = -0^2+2\cdot0-2 = -0 + 0 - 2 = -2 $$

In this case x-intercept doesn't be since equation $-ten^two+2x-ii=0$ does not has the solutions (use quadratic equation solver to check ). So, in this example we volition plot the graph using only 2 points

5 2 On A Graph,

Source: https://www.mathportal.org/calculators/quadratic-equation/quadratic-function-grapher.php

Posted by: bennettriention77.blogspot.com

Share this post