Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

F(x)=3x2−16+21F(x)=3x^2-16+21 find the zeros of the function

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Convert equations of parabolas from general to vertex formright chevron icon

Full solution

Q. F(x)=3x2−16+21F(x)=3x^2-16+21 find the zeros of the function
  1. Write Function and Coefficients: Write down the given function and identify the coefficients.\newlineThe given function is F(x)=3x2−16x+21F(x) = 3x^2 - 16x + 21. The coefficients are a=3a = 3, b=−16b = -16, and c=21c = 21.
  2. Find Zeros: Set the function equal to zero to find the zeros. 0=3x2−16x+210 = 3x^2 - 16x + 21
  3. Factor Quadratic Equation: Factor the quadratic equation, if possible.\newlineTo factor, we look for two numbers that multiply to a∗ca*c (3∗21=633*21 = 63) and add to bb (−16-16).\newlineThe numbers that satisfy this are −9-9 and −7-7 because −9×−7=63-9 \times -7 = 63 and −9+−7=−16-9 + -7 = -16.
  4. Write Factored Form: Write the factored form of the equation.\newline0=3(x−7)(x−3)0 = 3(x - 7)(x - 3)
  5. Solve for x: Set each factor equal to zero and solve for x.\newlinex−7=0x - 7 = 0 or x−3=0x - 3 = 0\newlinex=7x = 7 or x=3x = 3

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

Question
What is the focus of the parabola y=−x2y = -x^2?\newlineSimplify any fractions.\newline(_____ , _____)\newline
Get tutor helpright-arrow

Posted 1 month ago

Question
The equation of a parabola is y=x2−10x+25y = x^2 - 10x + 25. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
In which direction does the parabola x+y2=−7x + y^2 = -7 open?\newlineChoices:\newline(A) up\text{up}\newline(B) down\text{down}\newline(C) right\text{right}\newline(D) left\text{left}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the vertex of the parabola y=−4(x−2)2+2y = -4(x - 2)^2 + 2??\newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the axis of symmetry of the parabola x=12(y+3)2+5x = \frac{1}{2}(y + 3)^2 + 5?
Get tutor helpright-arrow

Posted 2 months ago

Question
In which direction does the parabola x−2y2=−5x - 2y^2 = -5 open?\newlineChoices:\newline[A]up\text{[A]up}\newline[B]down\text{[B]down}\newline[C]right\text{[C]right}\newline[D]left\text{[D]left}
Get tutor helpright-arrow

Posted 2 months ago

Question
What is the vertex of the parabola y−8x2=4y - 8x^2 = 4? \newline(_,_)(\_,\_)
Get tutor helpright-arrow

Posted 1 month ago

Question
The equation of a circle is x2+(y+4)2=1 x^{2}+(y+4)^{2}=1 . What are the center and radius of the circle?\newlineChoose 11 answer:\newline(A) The center is (−4,0) (-4,0) and the radius is 11 .\newline(B) The center is (4,0) (4,0) and the radius is 11 .\newline(C) The center is (0,4) (0,4) and the radius is 11 .\newline(D) The center is (0,−4) (0,-4) and the radius is 11 .
Get tutor helpright-arrow

Posted 4 months ago

Question
y=(x−3)(x+9) y=(x-3)(x+9) \newlineThe given equation is graphed in the xy x y -plane. Which of the following are x x -intercepts of the graph?\newlineChoose 11 answer:\newline(A) −3-3 and −9-9\newline(B) −3-3 and 99\newline(C) 33 and −9-9\newline(D) 33 and 99
Get tutor helpright-arrow

Posted 4 months ago

Question
If y=2x2−5x+7 y=2 x^{2}-5 x+7 is graphed in the xy x y -plane, which of the following characteristics of the graph is displayed as a constant or coefficient in the equation?\newlineChoose 11 answer:\newline(A) x x -intercept(s)\newline(B) y y -intercept\newline(C) x x -coordinate of the vertex\newline(D) y y -coordinate of the vertex
Get tutor helpright-arrow

Posted 4 months ago

View all (59)