The formula is y=ax^2+bx+c
I also gave the wrong problems, they are...
1. y=x^2-4x
2. y=-x+1
3. y=x+1
4. y=2x^2
well for number one you said it was
y = -x^2 +1
when you graph it here are three points
(-1,0), (0,1),(1,0) so you know that the parabola is going downward. the axis of symmetry is the line in the middle of the parabola which would be : 0
the vertex point would be: (0,1)
I don't have my book with me but the formula for finding the axis of symmetry should be in your book. I can help you if you send it to me.
IDENTIFY THE AXIS OF SYMMETRY, CREATE A SUITABLE TABLE OF VALUES...
1. Y=-X^2+1
2. Y=2X
3. Y=-X^2+3X
4. Y=X^2+1
5. Y=X^2-4X
To find the axis of symmetry for a quadratic equation in the form y = ax^2 + bx + c, you can use the formula:
Axis of symmetry (x-value) = -b / (2a)
Let's apply this formula to each of the given quadratic equations:
1. For y = -x^2 + 1:
- In this equation, a = -1, b = 0, and c = 1.
- Plug these values into the formula:
Axis of symmetry (x-value) = -0 / (2(-1))
= 0
- So, the axis of symmetry for this parabola is the vertical line x = 0.
2. For y = 2x:
- In this equation, a = 0, b = 2, and c = 0.
- Plug these values into the formula:
Axis of symmetry (x-value) = -2 / (2(0))
= undefined
- Since there is no x^2 term, this equation represents a straight line and doesn't have an axis of symmetry.
3. For y = -x^2 + 3x:
- In this equation, a = -1, b = 3, and c = 0.
- Plug these values into the formula:
Axis of symmetry (x-value) = -3 / (2(-1))
= 3/2
- So, the axis of symmetry for this parabola is the vertical line x = 3/2.
4. For y = x^2 + 1:
- In this equation, a = 1, b = 0, and c = 1.
- Plug these values into the formula:
Axis of symmetry (x-value) = -0 / (2(1))
= 0
- So, the axis of symmetry for this parabola is the vertical line x = 0.
5. For y = x^2 - 4x:
- In this equation, a = 1, b = -4, and c = 0.
- Plug these values into the formula:
Axis of symmetry (x-value) = -(-4) / (2(1))
= 4/2
= 2
- So, the axis of symmetry for this parabola is the vertical line x = 2.
To create a suitable table of values, you can choose various x-values and calculate the corresponding y-values using the given quadratic equations. Substitute the chosen x-values into the equations and solve for y. You can choose any x-values, but it's usually helpful to choose symmetric values around the axis of symmetry to get a better understanding of the shape of the graph.