You are given a graph of a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ for different values of $a , b$, and $c$. For this function,
a. Determine whether the discriminant is positive, negative, or zero.
b. Determine if there are 0,1 , or 2 real solutions to $f ( x ) = 0$.
c. Solve the equation $f ( x ) = 0$.
-A grasshopper is perched on a reed 5 inches above the ground. It hops off the reed and lands on the ground about 7.9 inches away. During its hop, its height is given by the equation $$h = - 0.3 x ^ { 2 } + 1.75 x + 5$$ , where x is the
Distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of
The reed when it was 3.25 inches above the ground? Round to the nearest tenth.
A) 0.9 in.
B) 6.7 in.
C) 7.9 in.
D) 1.3 in.

Question

Quizplus · Accepted Answer

The discriminant is positive, so there are 2 real solutions to $f ( x ) = 0$. To solve the equation, we can use the quadratic formula: $x = \frac {-b \pm \sqrt {b^2 - 4ac}} {2a}$. Plugging in the values of $a$, $b$, and $c$, we get: $x = \frac {-1.75 \pm \sqrt {1.75^2 - 4(-0.3)(5)}} {2(-0.3)} = \frac {-1.75 \pm \sqrt {10.56}} {-0.6} = 0.9, 6.7$. Therefore, the grasshopper was 6.7 inches from the base of the reed when it was 3.25 inches above the ground.

You Are Given a Graph of a Function of the Form