Question

The factored form of a quadratic equation is y=(2x+1)(x-5), and the standard form is y=2x²-9x-5. Which of the following statements accurately describes the graph of y?
A) The x-intercepts are -1 and 5, and the y-intercept is -5.
B) The x-intercepts are -1/2 and 5, and the y-intercept is -5.
C) The x-intercepts are -1/2 and 5, and the y-intercept is 5.
D) The x-intercepts are 1 and -5, and the y-intercept is -5.

Answer 1

Answer:

B) The x-intercepts are -1/2 and 5,

and the y-intercept is -5.

Step-by-step explanation:

The intercept form of a quadratic equation y = ax² + bx + c:

$y=a(x-p)(x-q)$

$\text{x-intercepts:}\ p\ \text{and}\ q\\\\\text{y-intercept}:\ a(-p)(-q)$

We have the equation:

$y=2x^2-9x-5=(2x+1)(x-5)$

$2x+1=2\left(x+\dfrac{1}{2}\right)\to y=2\left(x+\dfrac{1}{2}\right)(x-5)$

$y=2\bigg(x-\left(-\dfrac{1}{2}\right)\bigg)(x-5)$

Therefore

$a=2\\\\x-intercepts:\ p=-\dfrac{1}{2}\ \text{and}\ q=5\\\\\text{y-intercept:}\ (2)\left(-\dfrac{1}{2}\right)(5)=-5$