Question

$f{x} = {x}^{2} - 4x + 3 \\ g{x} = {x }^{2} + 4x + 3 \\ h{x} = - {x}^{2} + 4$
draw the graph of the given quadratic equation ​

Answer 1

Answer:

p(x)=x

2

−4x+3

Finding the y-intercept

To find y-intercept of graph of p. We can find p(0)

p(x)=x

2

−4x+3

p(0)=(0)

2

−4(0)+3

P(0)=3

The y-intercept of graph of y=p(x) is (0,3)

Find the x-intercept

To find x-intercept, we can solve equation p(x)=0

0=x

2

−4x+3

Solving the above equation, we get

x=3, x=1

The x-intercept of graph of y=p(x) are (3,0) & (1,0)

The leading term of the polynomial is x

2

, & so the end behaviour of function p will be the same as the end behaviour of x

2

.

Since degree is even & the leading coefficient is positive, the end behaviour will be:

x→+∞, f(x)→+∞

x→−∞, f(x)→+∞.