Question

Draw the graph of quadratic polynomial

f(x) = x^2 - 5x + 6​

Answer 1

Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given quadratic polynomial is

$\rm \: f(x) = {x}^{2} - 5x + 6$

Let assume that

$\rm \: y = {x}^{2} - 5x + 6$

To plot the graph of the quadratic polynomial which is always parabola, the following steps have to be followed :-

Step :- 1 Vertex of parabola

We know, vertex of parabola of quadratic polynomial ax² + bx + c is given by

$\blue{ \boxed{\bf \:Vertex = \bigg( - \dfrac{ b}{2a} , \: \dfrac{4ac - {b}^{2} }{4a} \bigg)}}$

Here,

$\rm \: a = 1$

$\rm \: b = - \: 5$

$\rm \: c = 6$

So, on substituting the values, we get

$\rm \: \:Vertex = \bigg( - \dfrac{ ( - 5)}{2} , \: \dfrac{4(1)(6) - {( - 5)}^{2} }{4} \bigg)$

$\rm \: \:Vertex = \bigg(\dfrac{5}{2} , \: \dfrac{24 - 25 }{4} \bigg)$

$\rm \: \:Vertex = \bigg(\dfrac{5}{2} , \: - \: \dfrac{1}{4} \bigg)$

Step :- 2 Point of intersection with x - axis

We know, on x - axis, y = 0.

So, on substituting y = 0, in given polynomial, we get

$\rm \: {x}^{2} - 5x + 6 = 0$

$\rm \: {x}^{2} - 3x - 2x + 6 = 0$

$\rm \: x(x - 3) - 2(x - 3) = 0$

$\rm \: (x - 3)(x - 2) = 0$

$\rm\implies \:x = 3 \: \: or \: \: x = 2$

Hence, the point of intersection with x- axis is (2, 0) and ( - 3, 0).

Step :- 3 Point of intersection with y - axis.

We know, on y - axis, x = 0

So, on Substituting the value in given polynomial, we get

$\rm \: y = 0 - 0 + 6$

$\rm\implies \:y = 6$

Hence, the point of intersection with y- axis is (0, 6).

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 2 & \sf 0 \\ \\ \sf 3 & \sf 0 \\ \\ \sf 0 & \sf 6\\ \\ \sf 2.5 & \sf - 0.25 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.