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What is the vertex form of y=9x^2+14x+12? - Socratic y = 9(x+7 9)^2 +59 12 A quadratic is written in the form y= ax^2 +bx+c Vertex form is known as y = a(x+b)^2 +c, giving the vertex as (-b,c) It is useful to be able to change a quadratic expression into the form a(x+b)^2 +c The process is by completing the square y =9x^2 +14x+12" "larr the coefficient of x^2 must be 1 y =9(x^2 +14 9x +12 9) To make a square of a binomial, you need to add on
How do you solve 3x+4y=-4 and x+2y=2 using substitution? - Socratic See the entire solution process below: Step 1) Solve the second equation for x: x + 2y = 2 x + 2y - 2y = 2 - 2y x + 0 = 2 - 2y x = 2 - 2y Step 2) Substitute color(red)(2 - 2y) for x in the first equation and solve for y: 3(color(red)(2 - 2y)) + 4y = -4 6 - 6y + 4y = -4 6 - 2y = -4 6 - 6 - 2y = -4 - 6 0 - 2y = -10 -2y = -10 (-2y) color(red)(-2) = (-10) color(red)(-2) (color(red)(cancel(color
Solve this? - Socratic x = 1 or log_2 sqrt14 |2^(2x)-9|=5 So , +-[2^(2x)-9]=5 Take +(2^(2x)-9)=5 =>2^(2x)=14 =>log_2 14=2x =>1 2log_2 14=x =>log_2 14^(1 2)=x =>log_2 sqrt14=x Or -(2^(2x)-9
How do you graph y=-2(3+x)^2 +4? - Socratic The vertex form is y = a(x-h)^2 +k Rearrange your equation to y = -2(x+3)^2 +4 Then a=-2, h=-3, and k=4 Step 2 Find the vertex The vertex is at (h,k) or (-3,4) Step 3 Find the y-intercept Set x=0 and solve for y y=-2(3+x)^2+4 = -2(3)^2+4 = -2(9) +4 = -18+4 = -14 The y-intercept is at (0,-14) Step 4 Find the x-intercept(s)
4 14 x 10 12? - Socratic 5 21 You could first multiply the numerators: 4 xx 10 = 40 then the denominators: 14 xx 12 = 168 Now you have 4 14 xx 10 12 = 40 168 You could simplify that by dividing both sides by 4 40 4 = 10 168 4 = 42 So 40 168 = 10 42 Then simplify that more 10 2 = 5 42 2 = 21 Your final answer is 5 21