https://www.youtube.com/watch?v=CFjFixc6r_o (explain the whole video for my SAT study)
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Welcome to SAT Math preparation. Today we'll explore quadratic functions, which are fundamental to many SAT problems. A quadratic function has the standard form f of x equals a x squared plus b x plus c, where a is not equal to zero. The graph of any quadratic function is a parabola that opens upward when a is positive, or downward when a is negative.
The vertex form of a quadratic function is f of x equals a times the quantity x minus h squared plus k. In this form, h and k represent the coordinates of the vertex. The vertex form makes it easy to identify key features: the vertex is at point h comma k, the axis of symmetry is the vertical line x equals h, and the parameter a determines whether the parabola opens upward or downward.
Finding the roots and intercepts of quadratic functions is crucial for SAT problems. To find x-intercepts, also called roots or zeros, we set the function equal to zero and solve. We can use factoring, the quadratic formula, or completing the square. The y-intercept is simply the constant term c, found by setting x equal to zero. In this example, the parabola f of x equals x squared minus 3x plus 2 factors as x minus 1 times x minus 2, giving us roots at x equals 1 and x equals 2.