Question

what is the axis of symmetry for this quadratic function?

(f(x) = 5x^2 - 10x + 6)

(x = ?)

axis of symmetry: (x = \frac{-b}{2a})

simplify your answer completely.

Explanation:

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<reasoning>

Identify the coefficients of the quadratic function

To find the axis of symmetry, we first identify the coefficients \(a\), \(b\), and \(c\) from the standard form of the quadratic function \(f(x) = ax^2 + bx + c\).
Given:
\[f(x) = 5x^2 - 10x + 6\]
Comparing this to the standard form:
\[a = 5\]
\[b = -10\]
\[c = 6\]

Apply the axis of symmetry formula

The formula for the axis of symmetry of a parabola in standard form is:
\[x = \frac{-b}{2a}\]
Substituting our identified values \(a = 5\) and \(b = -10\) into the formula:
\[x = \frac{-(-10)}{2(5)}\]

Simplify the expression

Now we simplify the numerator and the denominator to find the final value of \(x\):
\[x = \frac{10}{10}\]
\[x = 1\]
This vertical line \(x = 1\) represents the axis of symmetry.
</reasoning>

<answer>
What is the axis of symmetry for this quadratic function?
\(f(x) = 5x^2 - 10x + 6\)
\(x =\) <blank>1</blank>
</answer>

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Answer:

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<reasoning>

Identify the coefficients of the quadratic function

To find the axis of symmetry, we first identify the coefficients \(a\), \(b\), and \(c\) from the standard form of the quadratic function \(f(x) = ax^2 + bx + c\).
Given:
\[f(x) = 5x^2 - 10x + 6\]
Comparing this to the standard form:
\[a = 5\]
\[b = -10\]
\[c = 6\]

Apply the axis of symmetry formula

The formula for the axis of symmetry of a parabola in standard form is:
\[x = \frac{-b}{2a}\]
Substituting our identified values \(a = 5\) and \(b = -10\) into the formula:
\[x = \frac{-(-10)}{2(5)}\]

Simplify the expression

Now we simplify the numerator and the denominator to find the final value of \(x\):
\[x = \frac{10}{10}\]
\[x = 1\]
This vertical line \(x = 1\) represents the axis of symmetry.
</reasoning>

<answer>
What is the axis of symmetry for this quadratic function?
\(f(x) = 5x^2 - 10x + 6\)
\(x =\) <blank>1</blank>
</answer>

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