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adoni [48]
3 years ago
7

Which of the following is true for the graph of the quadratic function f(x)=2x^2-10x+12

Mathematics
1 answer:
lana [24]3 years ago
4 0
To find the x-intercepts let f(x) = 0 and solve the equation. To find the y-intercept(s) let x = 0 and solve the equation. To find the vertex: the x coordinate of the vertex is -b/2a where a is the coefficient of the x^2 and b is the coefficient of x. Then, substitute the value you get for -b/2a for the x and solve for y. That will give you the x,y coordinates. 
4. a. Solve 2x^2 -10x + 12 =0. Either use the quadratic formula or factor. x = 2 and x = 3. But those are the intercepts. The points of the intercepts are (2,0) and (3,0), NOT the point (3,2). a cannot be true. 4b. In the equation, substitute 0 for x and solve. f(x) or y comes out to 12. b is correct. 4c. -b/2a = 10/4 which reduces to 5/2. Substitute 5/2 for x and evaluate to find y. y = -1/2. Your answers for 4 are b and c. 
5. a. Substitute 0 for x and solve. y = -6, so your y-intercept is (0.-6). a is correct b. Substitute 0 for y and solve. x = 2 and -1. b is correct. That means d is not. c. -b/2a = 3/6 = 1/2. Substitute 1/2 for x and solve for y. The vertex is (1/2, - 27/4), e is correct. Your answers for 5 are a,b, and e. 
7. Substitute 0 for x and solve for y. y = -16/5, so the y intercept is (0/-16/5) a is true. b. x-intercepts always have 0 for the y coordinate, so b is NOT true. c. Expand your binomial and put your equation in ax^2, + bx + c form. -b/2a is 6/5 divided by 3/5 which equals 3. Put 3 in for x and find y. Your answer should be -5, so c is true. d. Let f(x) =0. Solve you equation by using the quadratic formula or factoring. x comes out to be 8 and -2, so d is true. Your ansers for 7 are a,c, and d.
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Using Math.

Step-by-step explanation:

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See, you should have been more specific with your question, maybe said "What is the answer" not "How do I solve".

But I guess I'll help you out bro

<em>Multiply</em> both sides by 6

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then <em>multiply</em> both sides by -1

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Read 2 more answers
For f(x) = 3x +1 and g(x) = x2 – 6, find (f- g)(x).
Fiesta28 [93]

Answer:

\boxed{\sf (f-g)(x) = -{x}^{2}  + 3x + 7}

Given:

\sf f(x) = 3x + 1 \\ \sf g(x) =  {x}^{2}  - 6

To find:

\sf (f - g)(x) = f(x) - g(x)

Step-by-step explanation:

\sf \implies(f - g)x = f(x) - g(x) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = (3x + 1) - ( {x}^{2}  - 6) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = (3x + 1)  + (-  {x}^{2}  + 6) \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = 3x + 1 -  {x}^{2}  + 6 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    = - {x}^{2}  + 3x + 1 + 6 \\  \\ \sf \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:    =  -{x}^{2}  + 3x + 7

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3 years ago
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