4.1+-4.2+Graph+Quadratic+Functions+in+Standard+Form+and+Vertex+Form

4.1 Quadratic Functions in Standard Form

**__Quadratic Function__** - is a function that can be written in **standard form** y=ax^2 + bx + c **( x= -b/2a)** __**Parabola**__ - The graph of a quadratic function. **__Vertex__** -the lowest or highest point on a parabola **__Axis of Symmetry__** - divides the in half **__Minimum Value__** - the lowest point on the parabola **__Maximum Value__** - the highest point on the parabola **__Zeros__** - the (x) value that makes the equation equal to zero

Here's a Link to help you remember the Quadratic Formula


 * __Maximum__ **


 * __ Minimum __**







4.2 Graph Quadratic Functions in Vertex or Intercept Form

**__Vertex Form__** - The form y=a(x-h)^2+k where the vertex of the graph is (h,k) and the axis of the symmertry is x=h. *The quadratric function "y=1/4(x+2)^2+5" is the vertex form **__Intercept Form__** - The form y=2(x-p)(x-q), where the x-intercepts of the graph are p and q. *The quadratic function "y=2(x+3)(x-1) is in intercept form.

F O I L

F - first terms O - outer terms I - Inner terms L - last terms

Change form intercept form to standard

write y=-2(x+5)(x-8) in standard form = -2(x+5)(x-8) **Step1:** write original functon = -2(x^2-8x+5x-40) **Step 2:** Multiply using FOIL = -2(x^2-3x+40) **Step3:** Combine like terms = 2x^2+6x+80 **Step4:** Distribute property

Change form vertex form to standard

write f(x)=4(x-1)^2+9 in standard f(x)=4(x-1)^2+9 **Step1:** write original function =4(x-1)(x-1)+9 **Step2:** rewrite (x-1)^2 =4(x^2-x-x+1)+9 **Step3:** multiply using FOIL =4(x^2-2x+1)+9 **Step4:** combine like terms =4x^2-8x+4+9 **Step5:** distribute property =4x^2-8x+13 **Step6:** combine like terms

__//** Here's another link to help get you through this section!!! **//__ []

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