Answer to Question #328013 in Algebra for Busi

Question

The equations of three quadratic functions are given below:

(i) y = 2x2 + 12x + 18

(ii) y = −3x2 − 5x + 3

(iii) y = x2 + 2x − 5

Determine the discriminant of each function and the number of x-intercepts that the parabola has. Choose

the correct sentence. The function described in

[1] (i) has no discriminant and the parabola has no x-intercepts

[2] (ii) has a negative discriminant and the parabola has two x-intercepts

[3] (i) has a zero discriminant and the parabola has one x-intercept

[4] (iii) has a positive discriminant and the parabola has one x-intercept

Answer 1

The discriminant formula of a quadratic function y = ax² + bx + c is D = b² - 4ac.

$\text{(i) }y=2x^2+12x+18\\ D=12^2-4\cdot2\cdot18=0\\ \text{The parabola has one x-intercept.}$

$\text{(ii) }y=-3x^2-5x+3\\ D=(-5)^2-4\cdot(-3)\cdot3=61>0\\ \text{The parabola has two x-intercepts.}$

$\text{(iii) }y=x^2+2x-5\\ D=2^2-4\cdot1\cdot(-5)=24>0\\ \text{The parabola has two x-intercepts.}$

The correct sentence is [3] (i) has a zero discriminant and the parabola has one x-intercept.