SOLUTION: Find the vertex and intercepts for the quadratic function y=x^2+x-6. Sketch the graph, and state the domain and range. Any help is greatly appreciated.

Question 7124: Find the vertex and intercepts for the quadratic function y=x^2+x-6. Sketch the graph, and state the domain and range. Any help is greatly appreciated.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
To find the x-intercepts (the zeros), set the quadratic = 0 and solve for x:
Factor.
Apply the zero product principle.
,
,
The x-intercepts are: (-3, 0) and (2, 0)
The x-coordinate of the vertex is at: -b/2a = -1/2. (ax^2 + bx + c = 0)Substitute this into the quadratic equation and solve for the y-coordinate.

= - 6 1/4
The vertex is at: (-1/2, -6 1/4)
The graph of this quadratic equationis:

The domain (the set all possible values of the independent variable, that's x) is the set of all real numbers.
The range (the set of all possible values of the dependent variable, that's y) is also the set of all real numbers.
RELATED QUESTIONS
help on this graph needed, please! For the quadratic function y= f(x)= x^2-2x-15,... (answered by funmath)

For the quadratic function : f(x) = 2x^2 - 4x -6, find: a. The x intercepts and the y... (answered by solver91311)

Thank you for your help! Sketch each function. State the domain, range, values of... (answered by Fombitz)

Use transformations to sketch the function y=-3(2^x+6). State the domain and... (answered by CubeyThePenguin)

given the rational function r(x)=(x^3-x^2)/x^3-3x-2) find the x and y intercepts find... (answered by lwsshak3)

graph the quadratic function, and state its domain and range... (answered by Ave)

(a) Express the quadratic function in standard form. (b) Find its vertex and its x and y (answered by stanbon)

7. Sketch graph of each function and state the domain and range y= (x)-4 (answered by mersha)