Presentation on theme: "Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored?"— Presentation transcript:
Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you solve quadratic equations that can’t be factored? Standard: MM2A4.b.
Let’s look at some examples where x 2 is already by itself.
Examples. Solve the equation. Write the solutions as integers if possible. Otherwise, write them as radical expressions.
Let’s look at some examples where x 2 is NOT by itself.
We must solve to get x 2 by itself 1 st !
Falling object model When an object is dropped, the speed with which it falls continues to increase. Ignoring air resistance, its height h can be approximated by the falling object model:
An engineering student is a contestant in an egg dropping contest. The goal is to create a container for an egg so it can be dropped from a height of 32 feet without breaking (s = starting height). Find the time (t) it will take for the egg to hit the ground (height = ? ). Disregard air resistance. SOLUTION: The starting height is 32 feet. Now, substitute 0 for h and solve. Subtract 32 from both sides Divide both sides by –16 Take the square root of both sides So, the answer is 1.4 seconds. It is only the positive of the square root b/c you can’t have negative seconds!!!!!
The following quadratics are in standard form, ax 2 + bx + c Evaluate b 2 – 4ac for each of the following )x 2 – 3x + 2 2)x 2 – 4x + 4 3)2x 2 – 3x + 3
There is a way to tell how many roots an equation will have. It’s called finding the discriminant. The discriminant is a small part of the quadratic formula.
If the answer is POSITIVE, then you will have 2 roots. If the answer is ZERO, then you will have 1 root. If the answer is NEGATIVE, then you will have no roots. Our text book says solutions instead of roots (same thing).
Determine the number of roots. Example: 1
Determine the number of roots. Example: 2
Determine the number of roots. Example: 3
Find the number of x-intercepts. Example: 4
Find the number of x-intercepts. Example: 5
Solve for x:
Quadratic Formula: gives the solution of in terms of the coefficients a, b & c. The solutions of the quadratic equation are
Ex: 1 Solve x 2 + 9x +14 = 0 a = b = c = 1 st 2 nd
-5/2 & 2 -1 & & -1.39
A rocket is shot upward with an initial velocity of 125 feet per second from a platform 3 feet above the ground. Use the model to find how long it will take the rocket to hit the ground. 3 ft t = 7.83 seconds