Solving Quadratic Equations using the Quadratic Formula

a

We need to match the function

f (x) = x^{2} - 4 x + 2

with its graph just by using the discriminant.

Discriminant : b^{2} - 4 a c

In our case,

a = 1,

b = - 4,

and

c = 2 .

b^{2} - 4 a c

SubstituteValuesSubstitute values

(- 4)^{2} - 4 (1) (2)

CalcPowProdCalculate power and product

16 - 8

SubTermsSubtract terms

8

The discriminant is positive, so the graph of the function

f (x) = x^{2} - 4 x + 2

intercepts the

x

-axis twice. Consequently, the graph of this function is option II.

b

In this part we need to match the function

f (x) = x^{2} - 4 x + 4

with its graph just by using the discriminant.

Discriminant : b^{2} - 4 a c

This time

a = 1,

b = - 4,

and

c = 4 .

b^{2} - 4 a c

SubstituteValuesSubstitute values

(- 4)^{2} - 4 (1) (4)

CalcPowProdCalculate power and product

16 - 16

SubTermsSubtract terms

0

Since the discriminant is zero, the graph of the function

f (x) = x^{2} - 4 x + 4

intercepts the

x

-axis only once. Consequently, the graph of this function is option III.

c

Finally, we will match the function

f (x) = x^{2} - 4 x + 6

with its graph just by using the discriminant.

Discriminant : b^{2} - 4 a c

This time

a = 1,

b = - 4,

and

c = 6 .

b^{2} - 4 a c

SubstituteValuesSubstitute values

(- 4)^{2} - 4 (1) (6)

CalcPowProdCalculate power and product

16 - 24

SubTermsSubtract terms

- 8

Since the discriminant is negative, the graph of function

f (x) = x^{2} - 4 x + 6

does not intercept the

x

-axis. This implies that the graph of this function is option I.

Solving Quadratic Equations using the Quadratic Formula 1.19 - Solution