7.2-Graphing Quadratics

The X-INTERCEPTS (ZEROS) are the points where the graph of the quadratic function intersects the x-axis. They can be found by solving the equation f(x) = 0.

To determine the QUADRATIC FUNCTION from a graph, identify the vertex and the direction of the parabola (upward or downward). Use the vertex form or standard form to write the equation.

The AXIS of SYMMETRY (AOS) can be found using the formula $$x = -\frac{b}{2a}$$ , where a and b are the coefficients from the standard form of the quadratic equation $$y = ax^2 + bx + c$$ .

The Y-INTERCEPT is the point where the graph intersects the y-axis. It can be found by evaluating the function at x = 0.

To find the X-INTERCEPTS, set $$y = 0$$ and solve the equation $$6x^2 + 4x - 9 = 0$$ using the quadratic formula.

The vertex of a parabola represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola.

The standard form of a quadratic function is $$f(x) = ax^2 + bx + c$$ , where a, b, and c are constants.

A quadratic function opens upwards if the coefficient 'a' is positive and downwards if 'a' is negative.

The roots of a quadratic equation correspond to the X-INTERCEPTS of its graph. If the roots are real and distinct, the graph intersects the x-axis at two points.

To convert from vertex form $$f(x) = a(x-h)^2 + k$$ to standard form, expand the equation and simplify to the form $$f(x) = ax^2 + bx + c$$ .