Question

Find the x-intercepts of the parabola with vertex (1,-17) and y-intercept (0,-16)...

Answer 1

To solve this problem you must apply the proccedure shown below:

1. You have that the standard form of the equation for a parabola is:

$y=a(x-h)^{2}+k$

Where $(h,k)$ is the vertex

2. Substitute the values shown into the equation:

$y=a(x-1)^{2} -17$

3. Now, substitute $y=-16$ and $x=0$ to calculate $a$:

$-16=a(0-1)^{2} -17\\ a=1$

4. Then, the equation of the parabola is:

$y=(x-1)^{2} -17$

5. To calculate the x-intecept $y$ must be $y=0$. Substitute it into the equation and solve for $x$:

$0=(x-1)^{2} -17\\ x^{2} -x-16=0\\ x=4.53; x=-3.53$

The answer is: $(4.53,0),(-3.53,0)$