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### Course: Algebra 1>Unit 14

Lesson 4: Vertex form

# Vertex form introduction

One of the common forms for quadratic functions is called vertex form, because it highlights the coordinates of the vertex of the function's graph.

## Want to join the conversation?

• How do you know if it is a downward or an upward facing parabola?
• I use a tactic that I found online - If its positive, it looks like a smile! if negative, it looks like a frown! Its actually quite handy if you ask me.
• How do you find the "a" value when there is no visible number in front of the parentheses? Ex. f(x)=(x+2)^2+4
• It is 1, because in math, everything is already inherently being multiplied by 1. There is a coefficient, it is one.
• i keep zoning out on this vid and then having to watch it over again
• same here
• How do you get from `"Quadratic Standard Form"` to `"Vertex Form"`? Is there a certain method or must you algebraically manipulate it until it's right?
• Hello! The "method" I was taught, was really just doing the algebra as follows:
Finding the vertex of the quadratic by using the equation x=-b/2a, and then substituting that answer for y in the orginal equation.

Then, substitute the vertex into the vertex form equation, y=a(x-h)^2+k. (a will stay the same, h is x, and k is y).
Also, remember that your h, when plugged into the equation, must be the additive inverse of what you got for x.

If I can further explain, please let me know.
Hope it helped!
• How do you know if an equation is a downward opening or upward opening? The constant term?
• You can tell from the quadratic term, the value of A in `y = Ax^2 + Bx + C` or `y = A(x - H)^2 + K`. If A is positive, the graph expands upward (we say that it is concave up). If A is negative, the graph expands downward (we say that it is concave down).
• At , Sal says in future he will explain how to get from Quadratic Standard Form to Vertex Form. Can anyone show me the link to that video? Thanks!
• Would it be correct to call a parabola positive or negative, and why is this so?
• I think it would, because it would indicate how the parabola is graphed.
• When we look at a quadratic equation, how can we tell if the parabola is positive or negative?
• For standard form: y=Ax^2+Bx+C
Look at the coefficient of the x^2 term. If "A" is positive, the parabola opens up. If "A" is negative, then the parabola opens down.

For Vertex Form: y=a(x-h)^2+k
The sign of "a" determines the direction of the parabola. If "a" is positive, the parabola opens up. If "a" is negative, the parabola opens down.

Hope this helps.
• How do you find vertex form from the graph of the quadratic function?
• 1) Make the function look like ax^2 + bx + c = 0.
2) Use the vertex formula to find it.
x = -b / 2a
3) Use the x value to find the y value.

Hope this helps! If you have any questions or need help, please ask! :)