Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

View step-by-step help

Convert equations of parabolas from general to vertex form

Full solution

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 $x = 3$ .

More problems from Convert equations of parabolas from general to vertex form

Question

What is the focus of the parabola

y = -x^2

\newline

Simplify any fractions.

\newline

(_____ , _____)

\newline

Posted 1 month ago

Question

The equation of a parabola is

y = x^2 - 10x + 25

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

Posted 2 months ago

Question

In which direction does the parabola

x + y^2 = -7

\newline

\newline

\text{up}

\newline

\text{down}

\newline

\text{right}

\newline

\text{left}

Posted 2 months ago

Question

What is the vertex of the parabola

y = -4(x - 2)^2 + 2

?

\newline

(\_,\_)

Posted 2 months ago

Question

What is the axis of symmetry of the parabola

x = \frac{1}{2}(y + 3)^2 + 5

Posted 2 months ago

Question

In which direction does the parabola

x - 2y^2 = -5

\newline

\newline

\text{[A]up}

\newline

\text{[B]down}

\newline

\text{[C]right}

\newline

\text{[D]left}

Posted 2 months ago

Question

What is the vertex of the parabola

y - 8x^2 = 4

\newline

(\_,\_)

Posted 1 month ago

Question

The equation of a circle is

x^{2}+(y+4)^{2}=1

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(-4,0)

and the radius is

1

\newline

(B) The center is

(4,0)

and the radius is

1

\newline

(C) The center is

(0,4)

and the radius is

1

\newline

(D) The center is

(0,-4)

and the radius is

1

Posted 4 months ago

Question

y=(x-3)(x+9)

\newline

The given equation is graphed in the

x y

-plane. Which of the following are

x

-intercepts of the graph?

\newline

1

\newline

-3

-9

\newline

-3

9

\newline

3

-9

\newline

3

9

Posted 4 months ago

Question

y=2 x^{2}-5 x+7

is graphed in the

x y

-plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?

\newline

1

\newline

x

\newline

y

\newline

x

-coordinate of the vertex

\newline

y

-coordinate of the vertex

Posted 4 months ago