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What is the axis of symmetry of [tex]$h(x) = 6x^2 - 60x + 147$[/tex]?

A. [tex]$x = -5$[/tex]
B. [tex][tex]$x = -3$[/tex][/tex]
C. [tex]$x = 3$[/tex]
D. [tex]$x = 5$[/tex]


Sagot :

To determine the axis of symmetry for the quadratic function [tex]\( h(x) = 6x^2 - 60x + 147 \)[/tex], we can use the formula for the axis of symmetry for a quadratic equation of the form [tex]\( ax^2 + bx + c \)[/tex]. The formula is:

[tex]\[ x = -\frac{b}{2a} \][/tex]

Here, [tex]\(a = 6\)[/tex] and [tex]\(b = -60\)[/tex]. Plugging these values into the formula, we get:

[tex]\[ x = -\frac{-60}{2 \cdot 6} \][/tex]

Simplify the expression inside the fraction:

[tex]\[ x = \frac{60}{12} \][/tex]

Now, divide 60 by 12:

[tex]\[ x = 5 \][/tex]

So, the axis of symmetry for the quadratic function [tex]\( h(x) = 6x^2 - 60x + 147 \)[/tex] is [tex]\( x = 5 \)[/tex].

Among the given choices:
- [tex]\( x = -5 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = 3 \)[/tex]
- [tex]\( x = 5 \)[/tex]

The correct answer is [tex]\( x = 5 \)[/tex].