QUADRATICS: STANDARD FORM

By: Saniti Sharma

Learning Goals

1.) Change standard form to vertex form (completing the square)
2.) Find the vertex (maximum/minimum value)
3.) Use quadratic formula to find the x-intercepts
4.) Learn the importance of the discriminant
5.) Graph quadratics using x-intercepts
6.) Apply to word problems

SUMMARY

COMPLETING THE SQUARE is when you change the first two terms of the standard form y=ax*+bx+c into a perfect square (vertex form) while maintaining the balance of original relation.

1.) Take coefficient of b (middle number) and divide it by 2 and square it.
2.) Then bracket the ax* and bx and find the common and take it out, which will be the a value.
3.) Put the number you get from square rooting in the equation and bracket it with the ax and b
4.) Make sure to do + and - of the number and leave the c out the bracket and solve

Eg. y=2x*+16x+3

y=2(x*+8x)+3
y=2(x*+8x+16-16)+3
y=2(x*+8x+16)-32+3
y=2(x*+8x+16)-29
Y=2(x+4)*-29

The vertex is (-4,-29)
The parabola is opening up so the minimum value will be (-29)




QUADRATIC FORMULA

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To solve this formula, you have to find a, b and c values from the standard form and plug them in the equation.

Eg. y=3x*+4x+7 a=3 b=4 c=7



DISCRIMINANT
-Is the (b*-4ac)/2a
-tells us if there's any possible solutions (x-intercepts)
-if discriminant is negative , there are no x-intercepts, the discriminant can't be squared
-if discriminant is 0, there will be one solution
-if discriminant is more than 0, there will be 2 solutions

QUADRATIC FORMULA EXAMPLES

2 solutions
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1 solution
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0 solution
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Using the Quadratic Formula

COMPLETING THE SQUARE EXAMPLE

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❖ Completing the Square - Solving Quadratic Equations ❖

WORD PROBLEM USING QUADRATIC FORMULA

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QUADRATICS UNIT TEST ASSESSMENT

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REFLECTION ON QUADRATICS

Quadratics are when lines are curved and are used to find a maximum or minimum point. Parabolas are used for bridges, domes, golf and many other objects.

Factoring connects to graphing because you can find the x intercepts by putting the equation = 0. Then, you add the x intercepts and divide them by 2 to find the Axis of symmetry and then plug in the x value in the equation to find y and plot the graph.

Vertex form connects to graphing because the vertex is already given. The h is the x value and k is the y value. Then, you can expand the equation and also find the x-intercepts and graph the parabola.

Standard form connects to graphing because you can use the quadratic formula to find the x-intercepts and use -b/2a to find the x value of the vertex. Then, you sub in that value to find the y. The c value in the equation is the y-intercept which is already given. That's how you can graph a parabola using standard form. You can also complete the square to find the vertex, (h,k) and then expand to find the x-intercepts or sub in 0 for x to find the y-intercept. Although the y-intercept is already given