Find the axis of symmetry for y=x^2+4x-7
Find the axis of symmetry for y=3x^2-18x+1
Find the axis of symmetry for y=5x^2+10+3
Determine if the vertex is a maximum or minimum and identify it y=2x^2-3
Determine etc etc for y=-x^2-2x
Determine etc etc for y=5x^2-10x+3
Find the zeros for the function y= -x^2+2x
Find the zeros etc for y=3x^2+12x+9
for y=ax^2+bx+c, vertex is at x = -b/2a
if you complete the square, and have
(y-k) = a(x-h)^2 then
the vertex is at (h,k)
the axis of symmetry goes through the vertex.
the sign of the x^2 term determines whether the vertex is a min or max.
So, what do you come up with?
To find the axis of symmetry for a quadratic equation in the form y = ax^2 + bx + c, you can use the formula:
x = -b / (2a)
1. For y = x^2 + 4x - 7:
a = 1, b = 4, and c = -7.
The axis of symmetry is x = -b / (2a) = -4 / (2 * 1) = -2.
2. For y = 3x^2 - 18x + 1:
a = 3, b = -18, and c = 1.
The axis of symmetry is x = -b / (2a) = -(-18) / (2 * 3) = 3.
3. For y = 5x^2 + 10 + 3:
The equation seems to be missing the coefficient of 'x'. If it is intended to be y = 5x^2 - 10x + 3, then:
a = 5, b = -10, and c = 3.
The axis of symmetry is x = -b / (2a) = -(-10) / (2 * 5) = 1.
To determine if the vertex is a maximum or minimum, you need to check the coefficient 'a':
4. For y = 2x^2 - 3:
Since the coefficient 'a' is positive (a = 2 > 0), the vertex represents a minimum.
5. For y = -x^2 - 2x:
The coefficient 'a' is negative (a = -1 < 0), so the vertex represents a maximum.
6. For y = 5x^2 - 10x + 3:
The coefficient 'a' is positive (a = 5 > 0), so the vertex represents a minimum.
The zeros of a quadratic equation represent the x-values where the graph crosses the x-axis (y = 0). To find the zeros, you can set the equation equal to zero and solve for 'x':
7. For y = -x^2 + 2x:
Setting y = 0, we have -x^2 + 2x = 0.
Factoring out 'x', we get x(-x + 2) = 0.
So, the zeros are x = 0 and x - 2 = 0, which gives x = 0 and x = 2.
8. For y = 3x^2 + 12x + 9:
Setting y = 0, we have 3x^2 + 12x + 9 = 0.
Dividing the equation by 3, we get x^2 + 4x + 3 = 0.
Factoring, we have (x + 3)(x + 1) = 0.
So, the zeros are x + 3 = 0 and x + 1 = 0, which gives x = -3 and x = -1.
By following these steps, you should be able to find the axis of symmetry, determine if the vertex is a maximum or minimum, and find the zeros for various quadratic equations.