Answer:
Y-coordinate of the vertex: y = -7
Step-by-step explanation:
We are given the following quadratic equation, y = x² + 6x + 2, where a = 1, b = 6, and c = 2.
The value of "a" (leading coefficient) provides the following important details about the graph of the given quadratic equation:
The given prompt also states that we can determine the x-coordinate of the vertex by using the follwing formula:
[tex]\displaystyle\mathsf{x\:=\:\Bigg[ \:\frac{-b}{2a}\:\Bigg]}[/tex]
Using the given values from our quadratic equation, where a = 1, and b = 6, simply substitute these into the formula:
Quadratic equation: y = x² + 6x + 2
a = 1, b = 6, and c = 2.
[tex]\displaystyle\mathsf{x\:=\:\Bigg[ \:\frac{-b}{2a}\:\Bigg]\:=\:\frac{-6}{2(1)}\:=\:\frac{-6}{2}\:=\:-3}[/tex]
Therefore, the value of the x-coordinate is -3.
Now that we have the value of our x-coordinate, simply substitute this into the given quadratic equation to find its corresponding y-coordinate:
Quadratic equation: y = x² + 6x + 2
⇒ y = (-3)² + 6(-3) + 2
⇒ y = 9 - 18 + 2
⇒ y = - 7
Hence, the value of the y-coordinate is -7, making our vertex occurring at point (-3, -7). The attached screenshot is the graph of y = x² + 6x + 2, where it shows that the vertex is the minumum point on the graph.
___________________________
Quadratic equation
Quadratic function
Vertex
Parabola
___________________________
Learn more about quadratic equations here:
https://brainly.com/question/10891829
