Chapter 4 Sections 4: Supplemental Lesson
Vertex Form of Quadratic Functions
The standard form of a parabola’s equation is generally expressed as: y = ax2 + bx + c.
a > 0, the parabola opens ____________
a < 0, the parabola opens ____________
The vertex form of a parabola’s equation is expressed as: y = a(x – h)2 + k.
(___, ___) is the vertex
There is a shortcut for graphing quadratic equations!!!!
1) Find the turning point and graph it.
2) From this point, and subsequent points, follow the pattern
3) Connect your points!
Ex. 1
Ex. 2
a = ___
a = ___
Slope =
Slope =
What if your function is not in vertex form?!
We can transform the equation into vertex form using a method called completing the
square.
Method 1:
Write the vertex form of y = x2 + 2x – 3
y = x2 + 2x – 3
1)Write the equation in the form ax2 + bx ____ = y +/- c
*Leave room to add a third term to this side.
2) Determine the number that will complete a
perfect – square trinomial. You can do this simply by
𝑏 2
finding the value of ( )
2
3)Add this number to each side of the equation.
4)Rewrite the perfect square trinomial as the square of a binomial.
5) Get y by itself. Your function is now in vertex form!
6) Graph the function.
a = ___
Slope =
Slope =
Method 2: Use of Calculator
Graph the function y = x2 + 2x – 3
Step 1: Go to the table of values and find the vertex.
x
y
vertex
Step 2: Use the form y = a(x – h)2 + k, and plug in “h” and k”.
Step 3: Pick the y-int from the equation and plug into y = a(x – h)2 + k for “x and “y” to solve
for a.
Problem 2: Write the vertex form of the equation y = 2x2 – 8x - 10
Method 1: Completing the Square
Method 2: plugging into y = a(x - h)2 + k
a = ___
a = ___
Slope =
Slope =
Graph the following quadratic functions without the aid of a calculator.
1) y = x2 + 10x + 24
2) y = x2 – 6x + 13
3) y = - x2 – 2x + 3
4) y = 2x2 + 8x + 16
5. Given a quadratic function with vertex (3, 4) and point on the parabola (5, -4), write and graph the function
equation in vertex form.
6. For the following equations, describe the transformation on the function and the vertex.
a) y = (x – 3)2 + 6
b) y = (x + 4)2 – 2
c) y = (x – 4)2 – 1
.