Question

consider the quadratic equation ( x^2 + 2x - 24 = 0 ).

1. how could you solve the equation using a graph? explain.

b. how could you solve the equation using a table? explain.
a. enter the function ( f(x) = x^2 + 2x - 24 ) into a graphing calculator or a spreadsheet, and find the ( y )-value(s) when ( x = 0 ).
b. enter the function ( f(x) = x^2 + 2x - 24 ) into a graphing calculator or a spreadsheet to make a table of values, and look for rows with ( y )-values equal to 0. if the ( y )-value crosses zero without equaling 0, decrease the increment size on the table until you find an exact solution or are close enough to approximate the solution.
c. enter the function ( f(x) = x^2 + 2x - 24 ) into a graphing calculator or a spreadsheet to make a table of values, and look for rows with ( y )-values equal to 0. if there are no rows with a 0 in the ( y )-column, the equation has no solutions.
d. enter the function ( f(x) = x^2 + 2x - 24 ) into a graphing calculator or a spreadsheet, and find the ( x )-values that have the same ( y )-value. if the ( y )-values cross the ( x )-values without being equal, decrease the increment size on the table until you find an exact solution or are close enough to approximate the solution.

Explanation:

a. To solve $x^2 + 2x - 24 = 0$ using a graph, first rewrite the equation as the function $f(x) = x^2 + 2x - 24$. Graph this quadratic function; the solutions are the x-values where the graph intersects the x-axis (where $f(x)=0$). These intersection points are the roots of the equation.
b. For solving using a table, use the function $f(x) = x^2 + 2x - 24$. Input this into a graphing calculator or spreadsheet to generate a table of x and corresponding f(x) values. Look for rows where $f(x)=0$; those x-values are exact solutions. If the f(x) values cross 0 without hitting it exactly, decrease the increment size of x-values to narrow down and approximate the solutions.

Answer:

a. Graph $f(x)=x^2+2x-24$; x-intercepts are solutions.
b. C. Enter the function $f(x) = x^2 + 2x - 24$ into a graphing calculator or a spreadsheet to make a table of values, and look for rows with y-values equal to 0. If the y-value crosses zero without equaling 0, decrease the increment size on the table until you find an exact solution or are close enough to approximate the solution.