find quadratic function for parabola with min val -8 and....

[barband318]

find a quadratic function f(X)=ax^2+bx+c for the parabola with minimum value-8 and x intercepts -3 and 1

 

[stapel]

find a quadratic function f(X)=ax^2+bx+c for the parabola with minimum value-8 and x intercepts -3 and 1

a) What is the minimum (or maximum) point on a parabola? So what point have they given you? Which of the coordinates of this point have they given you?

b) What is the relationship between the x-value of the point in (a), and the x-intercepts (if any) of a parabola? So what is the x-value of this point?

c) Given what you have determined in answer to (a) and (b), what is the value of f(-1)? What equation do you get when you evaluate f(-1), given that f(x) = ax[sup:2066j8vo]2[/sup:2066j8vo] + bx + c?

d) What is the relationship between x-intercepts and the solutions (or zeroes) of an equation? So what are the values of f(-3) and f(1)?

Your answers to (c) and (d) should have given you a system of three linear equations in the variables "a", "b", and "c". Solve it to find your function. :wink:

Eliz.

 

[Deleted member 4993]

Knowing the x-intercepts

\(\displaystyle x_1 \, and \, x_2\)

the equation of the parabola is

\(\displaystyle y = a\cdot(x \,- \, x_1)\cdot(x \, - \, x_2)\)

Now you have only one unknown!!