2a. [1 mark] Consider the quadratic function f (x) = ax2 +...

2a. [1 mark] Consider the quadratic function f (x) = ax2 + bx + 22 . The equation of the line of symmetry of the graph y = f (x) is x = 1.75 . Using only this information, write down an equation in terms of a and b. 2b. [1 mark] The graph intersects the x-axis at the point (-2 , 0). Using this information, write down a second equation in terms of a and b. 2c. [2 marks] Hence find the value of a and of b. 2d. [2 marks] The graph intersects the x-axis at a second point, P. Find the x-coordinate of P.

Transcript

00:01 Okay, if we're given a quadratic function, f of x equals a x squared plus b x plus 22, with a line of symmetry, x equals 1 .75.

00:09 So i'm going to use x equals negative b over 2a to write an equation in terms of a and b.

00:14 So negative, sorry, 1 .75 equals negative b over 2a.

00:20 So i can multiply both sides by 2a here.

00:22 Here so that i can have 1 .75 times 2 giving me 3 .5 a is equal to a negative b write down an equation in terms of a and b so i do have an equation in terms of a and b here i don't know if you need to change that to like 3 .5 a plus b equals 0 something like that we also have a point so for part so this is part a here for part b we have a point negative 2 0 that's on the graph so i plug those into my original function i'm gonna have 0 sorry yeah no sorry 0 is equal to a times a negative 2 squared plus b times a negative 2 plus 22 so 0 is equal to this will be a positive 4a minus 2b plus 22 thankfully this works but if i subtract 22 the other side negative 22 is equal to 4a minus 2b.

01:16 So now i have two equations.

01:18 I'm gonna use that to find the value of a and b here.

01:21 So if i multiply this by 2 and i bring it down here, i'm gonna have 0 is equal to 7a plus 2b.

01:30 Set up for elimination so that these will cancel out.

01:33 Negative 22 is equal to an 11a, divide by 11 and i i get negative 2 for a.

01:40 B, i can use either equation.

01:43 So i'm going to use this one right here.

01:45 So i have 3 .5 times a negative 2 plus b equals 0.

01:50 Negative 7 plus b equals 0.

01:54 So b is equal to 7...

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