Quadratics

Question 1

Standard form of a quadratic equation

Answer 1

a(x^2)+bx+c

Question 2

What is x value called (term) when f(x) = 0?

Answer 2

root, x-int

Question 3

Find the roots (if they are integers) of an equation given a(x^2)+bx+c

Answer 3

1. Find -b/a
2. Find c/a
3. Find any two multiples of c/a the product of the roots is always c/a
4. Check whether the multiples in step 3 add up to -b/a the sum of the roots is always -b/a
5. Step 4 is false, redo step 3 but with two different multiples
6. Continue until the multiples satisfy both step 3 and 4

Question 4

Find the vertex of a quadratic function given the roots

Answer 4

1. (Root1+Root2)/2 = x value of vertex *since vertex is the midpoint of a parabola, its x value is the avg of the roots
2. Plug in the x value to find the y value of the vertex

Question 5

Vertex form

Answer 5

Vertex form: y=a((x-h)^2)+k, where h is the x-value of the vertex a and k is the y value

Question 6

Find the vertex form of a quadratic given a(x^2)+bx+c

Answer 6

1. Make sure the leading coefficient is 1 by dividing everything by the constant a
2. Find b/2
3. Write a((x+b/2)^2)+c
4. Find b^2
5. Write a((x+b/2)^2)+c-((b/2)^2)
6. Subtract ((b/2)^2) from c to get k
7. Write a((x+b/2)^2)+k
8. Multiply all values by a (which was divided by in the beginning)

Question 7

What is the vertex of a(x^2)+bx+c?

Answer 7

x value: b/2

y value: c-((b/2)^2)=c-((b^2)/4)

Question 8

Find the exact # of solutions given a(x^2)+bx+c?

Answer 8

1. Find the discriminant (D)
   1a. D = (b^2)-4ac
2. Look at the sign
   2a. if the sign is (+), the # of solutions is 2
   2b. if the sign is (-), the # of solutions is none
   2c. If D=0, the # of solutions is 1

Question 9

Quadratic Equation

Answer 9

x=(-b±√((b^2)-4ac))/2a