Questions on Algebra: Graphs, graphing equations and inequalities answered by real tutors!

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graph: y = x squared - 4x - 3
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OK

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation ax^2+bx+c=0

(in our case 1x^2+-4x+-3 = 0

) has the following solutons:

$x[12] = (b+-sqrt( b^2-4ac ))/2\a$

For these solutions to exist, the discriminant b^2-4ac

should not be a negative number.

First, we need to compute the discriminant b^2-4ac

.

Discriminant d=28 is greater than zero. That means that there are two solutions: $x[12] = (--4+-sqrt( 28 ))/2\a$ .

$x[1] = (-(-4)+sqrt( 28 ))/2\1 = 4.64575131106459$
$x[2] = (-(-4)-sqrt( 28 ))/2\1 = -0.645751311064591$

Quadratic expression 1x^2+-4x+-3

can be factored:
1x^2+-4x+-3 = (x-4.64575131106459)*(x--0.645751311064591)

Again, the answer is: 4.64575131106459, -0.645751311064591. Here's your graph:
graph( 500, 500, -10, 10, -20, 20, 1*x^2+-4*x+-3 )

To be more clear, the solutions are:
2 + sqrt(7)

and