Solve Quadratics by Graphing

Front

What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What does it mean if a quadratic graph does not intercept the x-axis?

Back

It means the quadratic equation has no real solutions.

Front

What are the solutions of a quadratic equation called?

Back

The solutions are called roots, x-intercepts, or zeros.

Front

What is the shape of the graph of a quadratic equation?

Back

The graph is a U-shaped curve called a parabola.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

What is the axis of symmetry in a quadratic graph?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves.

Front

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

Back

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

Front

What is the difference between a maximum and minimum in a quadratic function?

Back

A maximum is the highest point of the parabola (opens downwards), while a minimum is the lowest point (opens upwards).

Front

What is the standard form of a quadratic equation?

Back

The standard form is y = ax² + bx + c.

Front

What is the factored form of a quadratic equation?

Back

The factored form is y = a(x - r1)(x - r2), where r1 and r2 are the roots.