y = x² to obtain y = -2 ( x + 5 )²- 3
y = (x − 6)(x − 4)
When x = 0, y = 24,
so the y-intercept is 24.
When y = 0, x = 4 or x = 6,
so the x-intercepts are 4 and 6.
Taking the average of the x-intercepts,
x = 5 is the axis of symmetry.
When x = 5, y = (5 − 6)(5 − 4) = −1,
so the vertex is (5, −1).
b
y = − x2 + x + 6
This is an upside-down parabola.
When x = 0, y = 6, so this is the y-intercept.
y= − x2 + x + 6= −(x2 − x − 6)= −(x − 3)(x + 2)
So the x-intercepts are 3 and −2.
Taking their average, the axis of symmetry is x = .
When x = , y = − + + 6 = 6 so the vertex is , 6.
c
y = 5x2 − 20x + 15
When x = 0 then y = 15.
y= 5 x2 − 20 x + 15= 5 (x2 − 4x + 3 )= 5 (x − 3)( x − 1)
So the two x-intercepts are x = 1 and x = 3.
Hence, the axis of symmetry is x = 2 and the vertex is (2, −5).
y = (x − 6)(x − 4)
When x = 0, y = 24,
so the y-intercept is 24.
When y = 0, x = 4 or x = 6,
so the x-intercepts are 4 and 6.
Taking the average of the x-intercepts,
x = 5 is the axis of symmetry.
When x = 5, y = (5 − 6)(5 − 4) = −1,
so the vertex is (5, −1).
b
y = − x2 + x + 6
This is an upside-down parabola.
When x = 0, y = 6, so this is the y-intercept.
y= − x2 + x + 6= −(x2 − x − 6)= −(x − 3)(x + 2)
So the x-intercepts are 3 and −2.
Taking their average, the axis of symmetry is x = .
When x = , y = − + + 6 = 6 so the vertex is , 6.
c
y = 5x2 − 20x + 15
When x = 0 then y = 15.
y= 5 x2 − 20 x + 15= 5 (x2 − 4x + 3 )= 5 (x − 3)( x − 1)
So the two x-intercepts are x = 1 and x = 3.
Hence, the axis of symmetry is x = 2 and the vertex is (2, −5).
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