Okay, so polynomials, quadratic equations, roots, and all that fancy stuff has got to be my weakest point in math. I have a many questions that may seem stupid of me to ask but please bear with me. Help is oh so greatly appreciated. I am not looking for direct answers, but instead I'm looking for hints and guides as I would be glad to solve these myself.
Firstly, my teacher gave me questions such as and . He has told me to find the number of real roots each equation has by not solving the equation. How do I do this exactly?
Secondly, my teacher gave me this equation: . He wants me to find the x and y intercepts, and which point they occur at. How do I do this?
Thirdly, how to I find the maximum and minimum value for this equation: ?
Fourthly, how do I construct an equation if this information is given: A quadratic function has (-1, 0) as one of its intercepts and (3, -5) as its vertex?
Lastly, how do I show my steps for this: what is the maximum product of two numbers that add to -10? What numbers yield this product? I got -5 and -5 with a maximum of 25 through the process of guess and check, but I'm not so sure how to construct an equation based off of that.
Thanks for the help and thanks for putting up with me. I don't really understand my teacher's explanations for things and as a student, I can't really pay for a private tutor. MHF is a great source of help. Thank you all.