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1. If a quadratic function with a vertex at [tex]\((2,3)\)[/tex] is graphed, what would be the line of symmetry?

A. [tex]\(y=2\)[/tex]
B. [tex]\(x=2\)[/tex]
C. [tex]\(x=3\)[/tex]
D. [tex]\(y=3\)[/tex]

Sagot :

GinnyAnsweridn
To determine the line of symmetry for a quadratic function with a given vertex, let's recall the general properties of a quadratic function.

The standard form of a quadratic function is:
[tex]\[ y = ax^2 + bx + c \][/tex]

However, the vertex form of a quadratic function, which is more useful for our purposes, is given by:
[tex]\[ y = a(x - h)^2 + k \][/tex]
where [tex]\( (h, k) \)[/tex] is the vertex of the quadratic function.

The line of symmetry (also known as the axis of symmetry) for a quadratic function in vertex form is a vertical line that passes through the vertex. This line is given by the equation:
[tex]\[ x = h \][/tex]

Given the vertex of the quadratic function is [tex]\( (2, 3) \)[/tex]:

- [tex]\( h = 2 \)[/tex]
- [tex]\( k = 3 \)[/tex]

So, the equation for the line of symmetry will be:
[tex]\[ x = 2 \][/tex]

Therefore, the correct answer to the question is:
[tex]\[ x = 2 \][/tex]
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