SOLUTION: find the vertex and intercept coordinates of the following. y=x^2-5x-4

Question 143459: find the vertex and intercept coordinates of the following.
y=x^2-5x-4
Answer by nabla(475) (Show Source): You can put this solution on YOUR website!
Set y=0 :
x^2-5x-4=0
Use the quadratic formula to find where y is zero (the x-intercepts):

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=41 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5.70156211871642, -0.701562118716424. Here's your graph:

To find the y intercept we set x=0;
0^2-5(0)-4=y
It follows that y=-4. Thus, (0,-4) is the y-intercept.
The vertex is x=-b/(2a) when the equation is in form ax^2+bx+c=0. Thus, 5/2=x is the vertex. Now, find the corresponding y coordinate for x=5/2.
(5/2)^2-5(5/2)-4=25/4-50/4-16/4=-41/4
Thus, the vertex is at (5/2,-41/4). The graph is above.
RELATED QUESTIONS
find vertex and intercept coordinates of the following... (answered by nabla)

find the coordinates of the vertex y=5x^2-1 (answered by josgarithmetic)

find the coordinates of the vertex & y-intercept of the parabola... (answered by Mathtut)

graph and find the vertex, y-intercept and line of symmetry of the following equation:... (answered by stanbon)

[ Find the x-intercept(s) and the coordinates of the vertex for the parabola y = x^2 + 2x (answered by TimothyLamb)

Find the x-intercept(s) and the coordinates of the vertex for the parabola... (answered by josgarithmetic)

Find the x-intercept(s) and the coordinates of the vertex for the parabola y=X^2+6x-7 (answered by josgarithmetic)

find the x-intercept(s) and he coordinates of the vertex for the parabola... (answered by solver91311)

Find the vertex, x- intercepts, and y- intercept of... (answered by Menjax)