Question

you can use a table to estimate the solutions of a quadratic equation. when the value of the function is positive for one value and negative for the second value, then there is at least one zero between the two values. example 4 solve by using a table use a table to solve $-x^{2}+5x - 1 = 0$. steps 1 and 2 enter the function and view the table. enter $-x^{2}+5x - 1$ in the $y=$ list. use the table window to find where the sign of y1 changes. the sign changes between $x = 0$ and $x=$ _. steps 3 and 4 edit the table settings and find a more accurate location. use tblset to change $\triangle tbl$ to 0.1 and look again for the sign change. repeat this for 0.01 and 0.001 to get a more accurate location of one zero. one zero is located at approximately $x=$ _ (continued on the next page)

Explanation:

Step1: Analizar la tabla inicial

En la primera tabla, cuando \(x = 0\), \(y_1=-1\) (negativo) y cuando \(x = 1\), \(y_1=3\) (positivo). Entonces, según el teorema del valor intermedio, hay un cero entre \(x = 0\) y \(x = 1\).

Step2: Analizar la tabla refinada

En la segunda tabla, vemos que cuando \(x = 0.209\), \(y_1\approx - 0.0013\) (casi cero y negativo) y cuando \(x = 0.21\), \(y_1 = 0.0059\) (positivo).

Answer:

La primera blank se llena con \(1\) y la segunda blank se llena con \(0.21\) (aproximadamente).