Solving Quadratics by graphing

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a'.

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, also known as the roots or zeros of the function.

Front

How can you find the x-intercepts of a quadratic function?

Back

You can find the x-intercepts by setting the quadratic equation equal to zero and solving for x.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the formula x = -b/(2a).

Front

What does it mean if a quadratic has no real solutions?

Back

If a quadratic has no real solutions, it means the parabola does not intersect the x-axis, which occurs when the discriminant (b² - 4ac) is less than zero.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the expression b² - 4ac that determines the nature of the roots of the quadratic equation.

Front

What are the possible values of the discriminant and their meanings?

Back

If the discriminant is positive, there are 2 real solutions; if it is zero, there is 1 real solution; if it is negative, there are no real solutions.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.