To determine Haley's function in standard form, we need to identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] that she used in the quadratic formula:
Given the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
From the formula provided:
[tex]\[ x = \frac{-(-10) \pm \sqrt{(-10)^2 - 4(7)(-2)}}{2(7)} \][/tex]
We can identify the coefficients as follows:
- The coefficient [tex]\( a \)[/tex] is the multiplier of 7 in the term [tex]\(4(7)(-2)\)[/tex], which indicates [tex]\( a = 7 \)[/tex].
- The coefficient [tex]\( b \)[/tex] is the value that resolves to 10 when negated, hence [tex]\( b = -10 \)[/tex].
- The coefficient [tex]\( c \)[/tex] is the value in the term [tex]\(-2\)[/tex] multiplied by 4 and [tex]\( a \)[/tex], indicating [tex]\( c = -2 \)[/tex].
Therefore, Haley's function in standard form is:
[tex]\[ f(x) = 7x^2 - 10x - 2 \][/tex]
Here, the coefficients are:
- [tex]\( a = 7 \)[/tex]
- [tex]\( b = -10 \)[/tex]
- [tex]\( c = -2 \)[/tex]
In summary, the function in standard form would be:
[tex]\[ f(x) = 7x^2 - 10x - 2 \][/tex]
