Question

at what value of x does the function given by $y = 3x^2 - 30x - 13$ take its minimum value?
$x = \square$
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Explanation:

Step1: Recall vertex formula for parabola

For a quadratic function \( y = ax^2 + bx + c \), the x - coordinate of the vertex (which is the minimum point when \( a>0 \)) is given by \( x=-\frac{b}{2a} \).
Here, \( a = 3 \) and \( b=- 30 \).

Step2: Substitute values into formula

Substitute \( a = 3 \) and \( b=-30 \) into \( x =-\frac{b}{2a} \).
We get \( x=-\frac{-30}{2\times3} \).

Step3: Simplify the expression

First, simplify the numerator and the denominator. The numerator \( -(-30)=30 \), and the denominator \( 2\times3 = 6 \). Then \( x=\frac{30}{6}=5 \).

Answer:

\( 5 \)