## The vertex formula of quadratic function y = ax square + BX square + C?

y=a[x+b/(2a)]+(b^2-4ac)/(4a)

### Who can teach me the quadratic function: y = the square of AX + BX + C (a is not equal to 0) where a, B and C satisfy a + B + C = 0 and 9a-3b + C = 0, then the symmetry axis of the quadratic function image

f(1)=a+b+c=0

f(3)=9a+3b+c=0

The square of function y = ax + BX + C intersects the X axis at (1,0), (3,0)

The symmetry axis point is half of the middle distance between X1 and x2

I.e. x = 2

### Find the square of quadratic function y = ax + BX + C, the axis of symmetry of the image and the coordinates of the fixed point

1. Parabola is an axisymmetric figure. The axis of symmetry is a straight line x = - B / 2A

The only intersection between the axis of symmetry and the parabola is the vertex P of the parabola

In particular, when B = 0, the symmetry axis of the parabola is the Y axis (i.e. the straight line x = 0)

2. The parabola has a vertex P, and the coordinate is p (- B / 2a), (4ac-b) ²)/ 4a )

When - B / 2A = 0, P is on the y-axis Δ= b ²- When 4ac = 0, P is on the x-axis

3. The quadratic term coefficient a determines the opening direction and size of the parabola

When a > 0, the parabola opens upward; when a < 0, the parabola opens downward

|A | the larger, the smaller the opening of the parabola

4. The primary term coefficient B and the secondary term coefficient a jointly determine the position of the axis of symmetry

When a and B have the same sign (i.e. AB > 0), the axis of symmetry is on the left of the y-axis; because if the axis of symmetry is on the left, the axis of symmetry is less than 0, that is, - B / 2a0, so B / 2a is less than 0, so a and B have different signs

In fact, B has its own geometric meaning: the slope k of the functional analytical formula (primary function) of the tangent of the parabola at the intersection of the parabola and the y-axis can be obtained by deriving the quadratic function

5. The constant term C determines the intersection of parabola and Y axis

Parabola intersects Y axis at (0, c)

6. Number of intersections between parabola and X-axis

Δ= b ²- When 4ac > 0, the parabola has two intersections with the X axis

Δ= b ²- When 4ac = 0, the parabola has an intersection with the X axis

### Given the quadratic function y = AX2 + BX + C (a ≠ 0), where a, B and C satisfy a + B + C = 0 and 9a-3b + C = 0, the symmetry axis of the quadratic function image is () A. x=-2 B. x=-1 C. x=2 D. x=1

Equation 9a-3b + C = 0 minus equation a + B + C = 0,

8a-4b = 0

According to the symmetry axis formula, the symmetry axis is x = − B

2a=-1．

Therefore, B

### Known quadratic function y = ax ²+ BX + C (a is not equal to 0), where a, B and C satisfy a + B + C = 0 and 9a-3b + C = 0, then the axis of symmetry of the quadratic function image is straight Given the quadratic function y = AX2 + BX + C, where a, B and C satisfy a + B + C = 0 and 9a-3b + C = 0, the axis of symmetry of the quadratic function image is a straight line_____

∵ a + B + C = 0 and 9a-3b + C = 0 ∵ 8a-4b = 0 ∵ B = 2A

∵ the axis of symmetry of the quadratic function image is x = - B / 2A

The axis of symmetry of the quadratic function image is a straight line x = - 1

### Given the quadratic function f (x) = ax ^ 2-bc + 1, (1) if the solution set of F (x) > 0 is (- 3,4), find the solution set of real numbers a and B Value; (2) If a is an integer, B = a + 2, and the function f (x) has exactly one zero on (- 2, - 1), find the value of A

(1) The solution set of F (x) > 0 is (- 3,4) to know a