# What are the important points needed to graph F(x)=3x^2+4x-1 ?

Oct 3, 2016

$y -$intercept and its reflection, $x -$intercept(s), and the vertex.

#### Explanation:

There are 5 points which you can determine which will allow you to sketch the curve of the parabola. You can find....

$1. \rightarrow$ the y-intercept. This is given by the constant ,c. Here c= -1.

$2. \rightarrow$ the x-intercept(s), Make $f \left(x\right) = y = 0$
Solve by factorising, completing the square or the quadratic formula.
IN this case, $x = - 1.549 \mathmr{and} x = 0.215$

$3. \rightarrow$ the axis of symmetry. $x = - \frac{b}{2 a}$
This gives the x-value of the turning point. Here, $x = - \frac{2}{3}$

$4. \rightarrow$ the Turning point (vertex). It lies on the axis of symmetry,
In this case, find $y = f \left(- \frac{2}{3}\right) = - 2 \frac{1}{3}$

$5. \rightarrow$ the mirror image of c. Every point on the parabola has a reflection in the axis of symmetry. It is the same distance from the axis of symmetry as $c$ IN this case $- \frac{2}{3}$
The mirror image of $c$ is the point $\left(- \frac{4}{3} , - 1\right)$

graph{3x^2+4x-1 [-5, 5, -2.5, 2.5]}