the zeros of a parabola are 6 and -5. if (-1, 3) is a point on the graph, which equation can be solved to…

the zeros of a parabola are 6 and -5. if (-1, 3) is a point on the graph, which equation can be solved to find the value of a in the equation of the parabola?\n3 = a(-1 + 6)(-1 - 5)\n3 = a(-1 - 6)(-1 + 5)\n-1 = a(3 + 6)(3 - 5)\n-1 = a(3 - 6)(3 + 5)

the zeros of a parabola are 6 and -5. if (-1, 3) is a point on the graph, which equation can be solved to find the value of a in the equation of the parabola?\n3 = a(-1 + 6)(-1 - 5)\n3 = a(-1 - 6)(-1 + 5)\n-1 = a(3 + 6)(3 - 5)\n-1 = a(3 - 6)(3 + 5)

Answer

Answer:

A. $3 = a(-1 + 6)(-1 - 5)$

Explanation:

Step1: Escribir la ecuación factoreada de la parábola

La ecuación factoreada de una parábola con ceros $x_1$ y $x_2$ es $y=a(x - x_1)(x - x_2)$. Aquí, $x_1 = 6$ y $x_2=-5$, entonces $y=a(x - 6)(x+5)$.

Step2: Sustituir el punto en la ecuación

Dado el punto $(-1,3)$, sustituimos $x=-1$ y $y = 3$ en $y=a(x - 6)(x + 5)$. Obtenemos $3=a(-1 - 6)(-1+5)$. Simplificando, $3=a(-7)(4)$. Pero también se puede escribir como $3=a(-1 + 6)(-1 - 5)$ al re - ordenar los factores.