SOLUTION: Given the functions: y= -x^2+5x-2 and y=x^2+5x-2 It is well known that the sign of the coefficient of the x^2 term determines whether the graph of the quadratic function wil

Question 1046618: Given the functions: y= -x^2+5x-2 and y=x^2+5x-2

It is well known that the sign of the coefficient of the x^2 term determines whether the graph of the quadratic function will have a "hill" or a "valley". On the basis of the present problem, which sign is associated with the hill? Supply an intuitive explanation for this.

Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

if you have
then its graph will either look like a �� or a ��
� if �� is positive, it will be a
� if �� is negative, it will be a
so,
sign is associated with the
sign is associated with the
-> ->-> sign-> it will be a
and
->->-> sign-> it will be a

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the negative coefficient of the x^2 term indicates that it will be a hill rather than a valley.

another way of describing it is that the quadratic equation opens down rather than up.

why is this?

x^2 is positive regardless if x is negative or positive.
therefore -x^2 is negative regardless if x is negative or positive.

the x^2 term is the most powerful term because, as x gets larger, the x^2 term gets progressively larger than any of the other terms in the equation.

it therefore dominates at both extremes of the graph.

here's what the graph of -x^2 + 5x - 2 looks like.

here's what the graph of x^2 + 5x - 2 looks like.

the quadratic equation will have a maximum or a minimum value at x = -b/2a.

this is derived from the standard form of the quadratic equation which is ax^2 + bx + c = 0

when the equation is -x^2 + 5x - 2, the maximum value of the equation is when x = -5/-2 = 2.5.

the value of y would be -(2.5)^2 + 5*(2.5) - 2 = 4.25

when the equation is x^2 + 5x - 2, the minimum value of the equation is when x = -5/2 = -2.5.

the value of y would be (-2.5)^2 -5*2.5 - 2 = -8.25

you can see that from the graphs.

RELATED QUESTIONS
Find the degree, the leading term, the leading coefficient, the constant term, and the... (answered by josgarithmetic)
Okay well I have broken down the equation of Y=-5x^2+30x-36 Down to Y=-5(x^2-6x)-36... (answered by mananth,josgarithmetic)
Given f(x)=4(x-3)^2 (x+2)^3 (5x-1), determine The degree of the polynomial The... (answered by josgarithmetic)
What is a quartic function with only the two real zeros given? x = -4 and x = -1 A. (answered by ewatrrr)
What is a quartic function with only the two real zeros given? x = -4 and x = -1 A. (answered by ewatrrr)
which of the quadratic functions has the widest graph? a) y = 1/3 x^2 b) y = -4x^2 c) (answered by stanbon,advanced_Learner)
what is the center of... (answered by RoRo Jaxson)
what is the x-intercept of... (answered by josgarithmetic)
what is the range of y= -x^2-5x+6 (answered by josmiceli)