The discriminant of a quadratic equation is b^2-4ac.
Discriminant: - 14.71
No, see solution.
Practice makes perfect
To determine if Eva will reach a height of 10 feet, we first need to substitute 10 for h into the given equation.
h=- 16t^2 +22.3t+2
⇓
10 = - 16t^2 +22.3t+2
Since we are not interested in the solutions themselves, we will use the discriminant of the quadratic equation to determine the number of solutions if exist. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0
⇕
x=- b±sqrt(b^2-4ac)/2a
Let's first rewrite the given equation in standard form.
Having rewritten the equation, we can now identify the values of a, b, and c.
10 = - 16t^2 +22.3t+2
⇕
0= - 16t^2 + 22.3t+ ( - 8)
Finally, let's evaluate the discriminant.
Since the discriminant is - 14.71, the quadratic equation has no real solutions. Therefore, Eva will not reach a height of 10 feet.
Extra
Further information
If the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions.
