Solving 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 to solve a quadratic equation by graphing?

Back

Solving a quadratic equation by graphing involves plotting the quadratic function on a coordinate plane and identifying the points where the graph intersects the x-axis, which represent the solutions.

Front

What are the key components of a quadratic equation?

Back

The key components are the coefficients a, b, and c, where a is the coefficient of x², b is the coefficient of x, and c is the constant term.

Front

How do you find the vertex of a quadratic function?

Back

The vertex can be found using the formula (-b/2a, f(-b/2a)), where f(x) is the quadratic function.

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 equation x = -b/2a.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two real solutions; if D = 0, there is one real solution; if D < 0, there are no real solutions.

Front

How do you convert a quadratic equation to vertex form?

Back

A quadratic equation can be converted to vertex form y = a(x - h)² + k by completing the square.

Front

What is the standard form of a quadratic equation?

Back

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

Front

What are the solutions of the quadratic equation x² + 6x - 13 = 3?

Back

The solutions are x = -3 + √22 and x = -3 - √22.

Front

How do you determine the y-intercept of a quadratic function?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives the value of c in the equation y = ax² + bx + c.