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$F(x)=3x^2-16+21$ find the zeros of the functions

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Convert equations of parabolas from general to vertex form

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Q.

F(x)=3x^2-16+21

find the zeros of the functions

Write Function: Write down the given function. $\newline$ We are given the function $F(x) = 3x^2 - 16x + 21$ and we need to find its zeros.
Set Equation: Set the function equal to zero to find the zeros. $\newline$ To find the zeros of the function, we need to solve the equation $3x^2 - 16x + 21 = 0$ .
Factor Quadratic: Factor the quadratic equation. $\newline$ We look for two numbers that multiply to $3 \times 21$ ( $63$ ) and add up to $-16$ . These numbers are $-9$ and $-7$ . $\newline$ So we can write the equation as $3x^2 - 9x - 7x + 21 = 0$ .
Group and Factor: Group the terms to factor by grouping. $\newline$ We group the terms as $(3x^2 - 9x) - (7x - 21) = 0$ . $\newline$ Then we factor out the common factors from each group: $3x(x - 3) - 7(x - 3) = 0$ .
Factor Binomial: Factor out the common binomial factor. $\newline$ We can now factor out the common binomial factor $(x - 3)$ , which gives us $(3x - 7)(x - 3) = 0$ .
Solve for x: Solve for x. $\newline$ We set each factor equal to zero: $3x - 7 = 0$ and $x - 3 = 0$ . $\newline$ Solving the first equation for x gives us $x = \frac{7}{3}$ . $\newline$ Solving the second equation for x gives us $x = 3$ .

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