select the correct answer from each drop - down menu. what is the equation of the quadratic function…

select the correct answer from each drop - down menu. what is the equation of the quadratic function represented by this table?\n|x|y|\n|-3|3.75|\n|-2|4|\n|-1|3.75|\n|0|3|\n|1|1.75|\ny = □(x - □)^2+□

select the correct answer from each drop - down menu. what is the equation of the quadratic function represented by this table?\n|x|y|\n|-3|3.75|\n|-2|4|\n|-1|3.75|\n|0|3|\n|1|1.75|\ny = □(x - □)^2+□

Answer

Explanation:

Step1: Identify the vertex

The vertex of a quadratic function in vertex - form $y = a(x - h)^2+k$ is the point $(h,k)$. Since the function has the same $y$-value for $x=-3$ and $x = - 1$, the axis of symmetry is $x=\frac{-3+( - 1)}{2}=-2$. When $x=-2$, $y = 4$, so the vertex is $(-2,4)$, and $h=-2,k = 4$.

Step2: Find the value of $a$

Substitute the vertex $(h=-2,k = 4)$ and another point, say $(0,3)$ into the vertex - form $y=a(x - h)^2+k$. We get $3=a(0+2)^2+4$. Simplify the equation: [ \begin{align*} 3&=4a + 4\ 4a&=3 - 4\ 4a&=-1\ a&=-\frac{1}{4}=-0.25 \end{align*} ]

Answer:

$y=-0.25(x + 2)^2+4$