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What happens to the parabola if a>0?
The parabola opens up
What happens to the parabola if a<0?
The parabola opens down
What happens to the parabola if lal >1?
The parabola is narrower than y=x²
What happens to the parabola if lal <1?
The parabola is wider than y=x²
In the standard form equation, what variable represents the y-intercept?
c
What is the graphing shortcut?
1-3-5
What is the difference between quadratics in vertex form and quadratics in standard form?
Vertex: y = a(x - h)²+k {5.1}
Standard: y = ax² + bx + c {5.2}
Standard: y = ax² + bx + c {5.2}
How do you find the Value of a quadratic in Standard form?
First, find the x-value (-b/2a), then plug it in the quadratic equation. If the [a] is positive in the equation, it will have a minimum value; if it is negative, it will have a maximum value.
How do you change the equation, f(x) = 3(x + 2)^2 - 8 in standard form?
1. Square Root
~ f(x) = 3(x + 2)^2 - 8
~ f(x) = 3(x + 2)(x + 2) - 8
2. FOIL
~ f(x) = 3(x + 2)(x + 2) - 8
~ f(x) = 3(x^2 + 2x + 2x + 4) - 8
3. Distribute
~ f(x) = 3(x^2 + 2x + 2x + 4) - 8
~ f(x) = 3x^2 + 6x + 6x + 4 - 8
4. Add Terms
~ f(x) = 3x^2 + [6x + 6x] + [4 - 8]
~ f(x) = 3x^2 + 12x - 4
~ f(x) = 3(x + 2)^2 - 8
~ f(x) = 3(x + 2)(x + 2) - 8
2. FOIL
~ f(x) = 3(x + 2)(x + 2) - 8
~ f(x) = 3(x^2 + 2x + 2x + 4) - 8
3. Distribute
~ f(x) = 3(x^2 + 2x + 2x + 4) - 8
~ f(x) = 3x^2 + 6x + 6x + 4 - 8
4. Add Terms
~ f(x) = 3x^2 + [6x + 6x] + [4 - 8]
~ f(x) = 3x^2 + 12x - 4
When would the parabola open upward?
If [a] is positive
When does a quadratic function have a minimum value?
When the function opens up
What is the formula to finding the axis of symmetry and the x value?
x= -b/2a
How do you tell whether the quadratic function has minimum value or maximum value?
If [a] in the function is a negative number, then the parabola will curve down. The function has a minimum value when [a] is positive. It has a maximum value when [a] is negative.
If the curve points down it has a what value?
Minimum value
If |a|>1, would the parabola be wider or narrower than the parent function?
Narrower
What is the standard form equation?
ax²+bx+c
In standard form, if a is less than 0, which way does the parabola open up?
The parabola opens down if the a is negative.
In standard form, can a = zero
No
If the curve points down will it have a maximum or a minimum?
It will have a maximum value
2x²+x+2 has a ______________________ value
Minimum value