10. f(x) = 2(x - 3)^2 + 1 a) Find the vertex of the parabola...

10. f(x) = 2(x - 3)^2 + 1 a) Find the vertex of the parabola (h, k) b) Line of symmetry c) x - intercepts (if there are any) d) y - intercept e) Find the minimum y value. f) Sketch and label the graph.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Transcript

00:01 Hi, today we are solving the question in which the function fx is equals to 2 into x -3 whole square plus 1.

00:10 Now, first of all we need to find the vertex of the parabola h or k.

00:17 So, we can use the vertex form of a quadratic equation which is given by f of x is equals to a into x -h whole square plus k.

00:33 Now, comparing both these equations, so we can conclude that therefore vertex h or k is given by minus 3, not minus 3, 3 and 1.

00:51 Now, similarly taking the line of symmetry.

00:58 So, line of symmetry, line of symmetry for a parabola in vertex form of the equation is given by x is equals to h.

01:15 So, in this case the line of symmetry is x is equals to 3.

01:21 So, therefore we can conclude that x is equals to 3.

01:26 Now, taking the next one.

01:29 So, here we need to find the x -intercepts of the equation.

01:34 So, solving the equation fx is equals to 0.

01:40 That means 2 into x -3 whole square plus 1 is equals to 0.

01:47 Now, taking from here x -3 whole square is equals to 1, minus 1.

02:01 So, from here solving it.

02:04 So, we can take it as x square plus 9 minus here it is taken as plus 1 only and here it is it is equals to 0.

02:22 So, x square plus 9 minus 6x plus 1 is equals to 0.

02:36 So, from here we get the equation as x square minus 6x plus 10 is equals to 0...

Question

10. f(x) = 2(x - 3)^2 + 1 a) Find the vertex of the parabola (h, k) b) Line of symmetry c) x - intercepts (if there are any) d) y - intercept e) Find the minimum y value. f) Sketch and label the graph.

Please give Ace some feedback